Daily Papers

Webly supervised learning has attracted increasing attention for its effectiveness in exploring publicly accessible data at scale without manual annotation. However, most existing methods of learning with web datasets are faced with challenges from label noise, and they have limited assumptions on clean samples under various noise. For instance, web images retrieved with queries of tiger cat (a cat species) and drumstick (a musical instrument) are almost dominated by images of tigers and chickens, which exacerbates the challenge of fine-grained visual concept learning. In this case, exploiting both web images and their associated texts is a requisite solution to combat real-world noise. In this paper, we propose Cross-modality Aligned Prototypes (CAPro), a unified prototypical contrastive learning framework to learn visual representations with correct semantics. For one thing, we leverage textual prototypes, which stem from the distinct concept definition of classes, to select clean images by text matching and thus disambiguate the formation of visual prototypes. For another, to handle missing and mismatched noisy texts, we resort to the visual feature space to complete and enhance individual texts and thereafter improve text matching. Such semantically aligned visual prototypes are further polished up with high-quality samples, and engaged in both cluster regularization and noise removal. Besides, we propose collective bootstrapping to encourage smoother and wiser label reference from appearance-similar instances in a manner of dictionary look-up. Extensive experiments on WebVision1k and NUS-WIDE (Web) demonstrate that CAPro well handles realistic noise under both single-label and multi-label scenarios. CAPro achieves new state-of-the-art performance and exhibits robustness to open-set recognition. Codes are available at https://github.com/yuleiqin/capro.

Clustering is an unsupervised learning problem that aims to partition unlabelled data points into groups with similar features. Traditional clustering algorithms provide limited insight into the groups they find as their main focus is accuracy and not the interpretability of the group assignments. This has spurred a recent line of work on explainable machine learning for clustering. In this paper we focus on the cluster description problem where, given a dataset and its partition into clusters, the task is to explain the clusters. We introduce a new approach to explain clusters by constructing polyhedra around each cluster while minimizing either the complexity of the resulting polyhedra or the number of features used in the description. We formulate the cluster description problem as an integer program and present a column generation approach to search over an exponential number of candidate half-spaces that can be used to build the polyhedra. To deal with large datasets, we introduce a novel grouping scheme that first forms smaller groups of data points and then builds the polyhedra around the grouped data, a strategy which out-performs simply sub-sampling data. Compared to state of the art cluster description algorithms, our approach is able to achieve competitive interpretability with improved description accuracy.

Topic models have been prevalent for decades with various applications. However, existing topic models commonly suffer from the notorious topic collapsing: discovered topics semantically collapse towards each other, leading to highly repetitive topics, insufficient topic discovery, and damaged model interpretability. In this paper, we propose a new neural topic model, Embedding Clustering Regularization Topic Model (ECRTM). Besides the existing reconstruction error, we propose a novel Embedding Clustering Regularization (ECR), which forces each topic embedding to be the center of a separately aggregated word embedding cluster in the semantic space. This enables each produced topic to contain distinct word semantics, which alleviates topic collapsing. Regularized by ECR, our ECRTM generates diverse and coherent topics together with high-quality topic distributions of documents. Extensive experiments on benchmark datasets demonstrate that ECRTM effectively addresses the topic collapsing issue and consistently surpasses state-of-the-art baselines in terms of topic quality, topic distributions of documents, and downstream classification tasks.

We investigate a general formulation for clustering and transductive few-shot learning, which integrates prototype-based objectives, Laplacian regularization and supervision constraints from a few labeled data points. We propose a concave-convex relaxation of the problem, and derive a computationally efficient block-coordinate bound optimizer, with convergence guarantee. At each iteration,our optimizer computes independent (parallel) updates for each point-to-cluster assignment. Therefore, it could be trivially distributed for large-scale clustering and few-shot tasks. Furthermore, we provides a thorough convergence analysis based on point-to-set maps. Were port comprehensive clustering and few-shot learning experiments over various data sets, showing that our method yields competitive performances, in term of accuracy and optimization quality, while scaling up to large problems. Using standard training on the base classes, without resorting to complex meta-learning and episodic-training strategies, our approach outperforms state-of-the-art few-shot methods by significant margins, across various models, settings and data sets. Surprisingly, we found that even standard clustering procedures (e.g., K-means), which correspond to particular, non-regularized cases of our general model, already achieve competitive performances in comparison to the state-of-the-art in few-shot learning. These surprising results point to the limitations of the current few-shot benchmarks, and question the viability of a large body of convoluted few-shot learning techniques in the recent literature.

Image clustering is one of the most important computer vision applications, which has been extensively studied in literature. However, current clustering methods mostly suffer from lack of efficiency and scalability when dealing with large-scale and high-dimensional data. In this paper, we propose a new clustering model, called DEeP Embedded RegularIzed ClusTering (DEPICT), which efficiently maps data into a discriminative embedding subspace and precisely predicts cluster assignments. DEPICT generally consists of a multinomial logistic regression function stacked on top of a multi-layer convolutional autoencoder. We define a clustering objective function using relative entropy (KL divergence) minimization, regularized by a prior for the frequency of cluster assignments. An alternating strategy is then derived to optimize the objective by updating parameters and estimating cluster assignments. Furthermore, we employ the reconstruction loss functions in our autoencoder, as a data-dependent regularization term, to prevent the deep embedding function from overfitting. In order to benefit from end-to-end optimization and eliminate the necessity for layer-wise pretraining, we introduce a joint learning framework to minimize the unified clustering and reconstruction loss functions together and train all network layers simultaneously. Experimental results indicate the superiority and faster running time of DEPICT in real-world clustering tasks, where no labeled data is available for hyper-parameter tuning.

Pairwise clustering, in general, partitions a set of items via a known similarity function. In our treatment, clustering is modeled as a transductive prediction problem. Thus rather than beginning with a known similarity function, the function instead is hidden and the learner only receives a random sample consisting of a subset of the pairwise similarities. An additional set of pairwise side-information may be given to the learner, which then determines the inductive bias of our algorithms. We measure performance not based on the recovery of the hidden similarity function, but instead on how well we classify each item. We give tight bounds on the number of misclassifications. We provide two algorithms. The first algorithm SACA is a simple agglomerative clustering algorithm which runs in near linear time, and which serves as a baseline for our analyses. Whereas the second algorithm, RGCA, enables the incorporation of side-information which may lead to improved bounds at the cost of a longer running time.

Deep clustering has exhibited remarkable performance; however, the overconfidence problem, i.e., the estimated confidence for a sample belonging to a particular cluster greatly exceeds its actual prediction accuracy, has been overlooked in prior research. To tackle this critical issue, we pioneer the development of a calibrated deep clustering framework. Specifically, we propose a novel dual-head deep clustering pipeline that can effectively calibrate the estimated confidence and the actual accuracy. The calibration head adjusts the overconfident predictions of the clustering head using regularization methods, generating prediction confidence and pseudo-labels that match the model learning status. This calibration process also guides the clustering head in dynamically selecting reliable high-confidence samples for training. Additionally, we introduce an effective network initialization strategy that enhances both training speed and network robustness. Extensive experiments demonstrate the proposed calibrated deep clustering framework not only surpasses state-of-the-art deep clustering methods by approximately 10 times in terms of expected calibration error but also significantly outperforms them in terms of clustering accuracy.

Clustering is a widely deployed unsupervised learning tool. Model-based clustering is a flexible framework to tackle data heterogeneity when the clusters have different shapes. Likelihood-based inference for mixture distributions often involves non-convex and high-dimensional objective functions, imposing difficult computational and statistical challenges. The classic expectation-maximization (EM) algorithm is a computationally thrifty iterative method that maximizes a surrogate function minorizing the log-likelihood of observed data in each iteration, which however suffers from bad local maxima even in the special case of the standard Gaussian mixture model with common isotropic covariance matrices. On the other hand, recent studies reveal that the unique global solution of a semidefinite programming (SDP) relaxed K-means achieves the information-theoretically sharp threshold for perfectly recovering the cluster labels under the standard Gaussian mixture model. In this paper, we extend the SDP approach to a general setting by integrating cluster labels as model parameters and propose an iterative likelihood adjusted SDP (iLA-SDP) method that directly maximizes the exact observed likelihood in the presence of data heterogeneity. By lifting the cluster assignment to group-specific membership matrices, iLA-SDP avoids centroids estimation -- a key feature that allows exact recovery under well-separateness of centroids without being trapped by their adversarial configurations. Thus iLA-SDP is less sensitive than EM to initialization and more stable on high-dimensional data. Our numeric experiments demonstrate that iLA-SDP can achieve lower mis-clustering errors over several widely used clustering methods including K-means, SDP and EM algorithms.

The agriculture sector is essential for every country because it provides a basic income to a large number of people and food as well, which is a fundamental requirement to survive on this planet. We see as time passes, significant changes come in the present era, which begins with Green Revolution. Due to improper knowledge of plant diseases, farmers use fertilizers in excess, which ultimately degrade the quality of food. Earlier farmers use experts to determine the type of plant disease, which was expensive and time-consuming. In today time, Image processing is used to recognize and catalog plant diseases using the lesion region of plant leaf, and there are different modus-operandi for plant disease scent from leaf using Neural Networks (NN), Support Vector Machine (SVM), and others. In this paper, we improving the architecture of the Neural Networking by working on ten different types of training algorithms and the proper choice of neurons in the concealed layer. Our proposed approach gives 98.30% accuracy on general plant leaf disease and 100% accuracy on specific plant leaf disease based on Bayesian regularization, automation of cluster and without over-fitting on considered plant diseases over various other implemented methods.

The problem of Novel Class Discovery (NCD) consists in extracting knowledge from a labeled set of known classes to accurately partition an unlabeled set of novel classes. While NCD has recently received a lot of attention from the community, it is often solved on computer vision problems and under unrealistic conditions. In particular, the number of novel classes is usually assumed to be known in advance, and their labels are sometimes used to tune hyperparameters. Methods that rely on these assumptions are not applicable in real-world scenarios. In this work, we focus on solving NCD in tabular data when no prior knowledge of the novel classes is available. To this end, we propose to tune the hyperparameters of NCD methods by adapting the k-fold cross-validation process and hiding some of the known classes in each fold. Since we have found that methods with too many hyperparameters are likely to overfit these hidden classes, we define a simple deep NCD model. This method is composed of only the essential elements necessary for the NCD problem and performs impressively well under realistic conditions. Furthermore, we find that the latent space of this method can be used to reliably estimate the number of novel classes. Additionally, we adapt two unsupervised clustering algorithms (k-means and Spectral Clustering) to leverage the knowledge of the known classes. Extensive experiments are conducted on 7 tabular datasets and demonstrate the effectiveness of the proposed method and hyperparameter tuning process, and show that the NCD problem can be solved without relying on knowledge from the novel classes.

Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies can be achieved by reducing the input space if a minimal loss of information can be achieved. Clustering algorithms, in general, face two common problems: 1) these converge to different settings with different initial conditions and; 2) the number of clusters has to be arbitrarily decided beforehand. This problem has become critical in the realm of big data. Recently, clustering algorithms have emerged which can speedup computations using parallel processing over the grid but face the aforementioned problems. Goals: Our goals are to find methods to cluster data which: 1) guarantee convergence to the same settings irrespective of the initial conditions; 2) eliminate the need to establish the number of clusters beforehand, and 3) can be applied to cluster large datasets. Methods: We introduce a method that combines probabilistic and combinatorial clustering methods to produce repeatable and compact clusters that are not sensitive to initial conditions. This method harnesses the power of k-means (a combinatorial clustering method) to cluster/partition very large dimensional datasets and uses the Gaussian Mixture Model (a probabilistic clustering method) to validate the k-means partitions. Results: We show that this method produces very compact clusters that are not sensitive to initial conditions. This method can be used to identify the most 'separable' set in a dataset which increases the 'clusterability' of a dataset. This method also eliminates the need to specify the number of clusters in advance.

An approach to improve neural network interpretability is via clusterability, i.e., splitting a model into disjoint clusters that can be studied independently. We define a measure for clusterability and show that pre-trained models form highly enmeshed clusters via spectral graph clustering. We thus train models to be more modular using a "clusterability loss" function that encourages the formation of non-interacting clusters. Using automated interpretability techniques, we show that our method can help train models that are more modular and learn different, disjoint, and smaller circuits. We investigate CNNs trained on MNIST and CIFAR, small transformers trained on modular addition, and language models. Our approach provides a promising direction for training neural networks that learn simpler functions and are easier to interpret.

Despite the growing popularity of explainable and interpretable machine learning, there is still surprisingly limited work on inherently interpretable clustering methods. Recently, there has been a surge of interest in explaining the classic k-means algorithm, leading to efficient algorithms that approximate k-means clusters using axis-aligned decision trees. However, interpretable variants of k-means have limited applicability in practice, where more flexible clustering methods are often needed to obtain useful partitions of the data. In this work, we investigate interpretable kernel clustering, and propose algorithms that construct decision trees to approximate the partitions induced by kernel k-means, a nonlinear extension of k-means. We further build on previous work on explainable k-means and demonstrate how a suitable choice of features allows preserving interpretability without sacrificing approximation guarantees on the interpretable model.

Driven by advances in recording technology, large-scale high-dimensional datasets have emerged across many scientific disciplines. Especially in biology, clustering is often used to gain insights into the structure of such datasets, for instance to understand the organization of different cell types. However, clustering is known to scale poorly to high dimensions, even though the exact impact of dimensionality is unclear as current benchmark datasets are mostly two-dimensional. Here we propose MNIST-Nd, a set of synthetic datasets that share a key property of real-world datasets, namely that individual samples are noisy and clusters do not perfectly separate. MNIST-Nd is obtained by training mixture variational autoencoders with 2 to 64 latent dimensions on MNIST, resulting in six datasets with comparable structure but varying dimensionality. It thus offers the chance to disentangle the impact of dimensionality on clustering. Preliminary common clustering algorithm benchmarks on MNIST-Nd suggest that Leiden is the most robust for growing dimensions.

Document clustering and topic modeling are two closely related tasks which can mutually benefit each other. Topic modeling can project documents into a topic space which facilitates effective document clustering. Cluster labels discovered by document clustering can be incorporated into topic models to extract local topics specific to each cluster and global topics shared by all clusters. In this paper, we propose a multi-grain clustering topic model (MGCTM) which integrates document clustering and topic modeling into a unified framework and jointly performs the two tasks to achieve the overall best performance. Our model tightly couples two components: a mixture component used for discovering latent groups in document collection and a topic model component used for mining multi-grain topics including local topics specific to each cluster and global topics shared across clusters.We employ variational inference to approximate the posterior of hidden variables and learn model parameters. Experiments on two datasets demonstrate the effectiveness of our model.

Clustering is a class of unsupervised learning methods that has been extensively applied and studied in computer vision. Little work has been done to adapt it to the end-to-end training of visual features on large scale datasets. In this work, we present DeepCluster, a clustering method that jointly learns the parameters of a neural network and the cluster assignments of the resulting features. DeepCluster iteratively groups the features with a standard clustering algorithm, k-means, and uses the subsequent assignments as supervision to update the weights of the network. We apply DeepCluster to the unsupervised training of convolutional neural networks on large datasets like ImageNet and YFCC100M. The resulting model outperforms the current state of the art by a significant margin on all the standard benchmarks.

A model involving Gaussian processes (GPs) is introduced to simultaneously handle multi-task learning, clustering, and prediction for multiple functional data. This procedure acts as a model-based clustering method for functional data as well as a learning step for subsequent predictions for new tasks. The model is instantiated as a mixture of multi-task GPs with common mean processes. A variational EM algorithm is derived for dealing with the optimisation of the hyper-parameters along with the hyper-posteriors' estimation of latent variables and processes. We establish explicit formulas for integrating the mean processes and the latent clustering variables within a predictive distribution, accounting for uncertainty on both aspects. This distribution is defined as a mixture of cluster-specific GP predictions, which enhances the performances when dealing with group-structured data. The model handles irregular grid of observations and offers different hypotheses on the covariance structure for sharing additional information across tasks. The performances on both clustering and prediction tasks are assessed through various simulated scenarios and real datasets. The overall algorithm, called MagmaClust, is publicly available as an R package.

Spherical k-Means is frequently used to cluster document collections because it performs reasonably well in many settings and is computationally efficient. However, the time complexity increases linearly with the number of clusters k, which limits the suitability of the algorithm for larger values of k depending on the size of the collection. Optimizations targeted at the Euclidean k-Means algorithm largely do not apply because the cosine distance is not a metric. We therefore propose an efficient indexing structure to improve the scalability of Spherical k-Means with respect to k. Our approach exploits the sparsity of the input vectors and the convergence behavior of k-Means to reduce the number of comparisons on each iteration significantly.

Local graph clustering methods aim to detect small clusters in very large graphs without the need to process the whole graph. They are fundamental and scalable tools for a wide range of tasks such as local community detection, node ranking and node embedding. While prior work on local graph clustering mainly focuses on graphs without node attributes, modern real-world graph datasets typically come with node attributes that provide valuable additional information. We present a simple local graph clustering algorithm for graphs with node attributes, based on the idea of diffusing mass locally in the graph while accounting for both structural and attribute proximities. Using high-dimensional concentration results, we provide statistical guarantees on the performance of the algorithm for the recovery of a target cluster with a single seed node. We give conditions under which a target cluster generated from a fairly general contextual random graph model, which includes both the stochastic block model and the planted cluster model as special cases, can be fully recovered with bounded false positives. Empirically, we validate all theoretical claims using synthetic data, and we show that incorporating node attributes leads to superior local clustering performances using real-world graph datasets.

Visualizations for scattered data are used to make users understand certain attributes of their data by solving different tasks, e.g. correlation estimation, outlier detection, cluster separation. In this paper, we focus on the later task, and develop a technique that is aligned to human perception, that can be used to understand how human subjects perceive clusterings in scattered data and possibly optimize for better understanding. Cluster separation in scatterplots is a task that is typically tackled by widely used clustering techniques, such as for instance k-means or DBSCAN. However, as these algorithms are based on non-perceptual metrics, we can show in our experiments, that their output do not reflect human cluster perception. We propose a learning strategy which directly operates on scattered data. To learn perceptual cluster separation on this data, we crowdsourced a large scale dataset, consisting of 7,320 point-wise cluster affiliations for bivariate data, which has been labeled by 384 human crowd workers. Based on this data, we were able to train ClusterNet, a point-based deep learning model, trained to reflect human perception of cluster separability. In order to train ClusterNet on human annotated data, we use a PointNet++ architecture enabling inference on point clouds directly. In this work, we provide details on how we collected our dataset, report statistics of the resulting annotations, and investigate perceptual agreement of cluster separation for real-world data. We further report the training and evaluation protocol of ClusterNet and introduce a novel metric, that measures the accuracy between a clustering technique and a group of human annotators. Finally, we compare our approach against existing state-of-the-art clustering techniques and can show, that ClusterNet is able to generalize to unseen and out of scope data.

Contrastive learning has been widely studied in sentence representation learning. However, earlier works mainly focus on the construction of positive examples, while in-batch samples are often simply treated as negative examples. This approach overlooks the importance of selecting appropriate negative examples, potentially leading to a scarcity of hard negatives and the inclusion of false negatives. To address these issues, we propose ClusterNS (Clustering-aware Negative Sampling), a novel method that incorporates cluster information into contrastive learning for unsupervised sentence representation learning. We apply a modified K-means clustering algorithm to supply hard negatives and recognize in-batch false negatives during training, aiming to solve the two issues in one unified framework. Experiments on semantic textual similarity (STS) tasks demonstrate that our proposed ClusterNS compares favorably with baselines in unsupervised sentence representation learning. Our code has been made publicly available.

The advent of large pre-trained models has brought about a paradigm shift in both visual representation learning and natural language processing. However, clustering unlabeled images, as a fundamental and classic machine learning problem, still lacks an effective solution, particularly for large-scale datasets. In this paper, we propose a novel image clustering pipeline that leverages the powerful feature representation of large pre-trained models such as CLIP and cluster images effectively and efficiently at scale. We first developed a novel algorithm to estimate the number of clusters in a given dataset. We then show that the pre-trained features are significantly more structured by further optimizing the rate reduction objective. The resulting features may significantly improve the clustering accuracy, e.g., from 57% to 66% on ImageNet-1k. Furthermore, by leveraging CLIP's multimodality bridge between image and text, we develop a simple yet effective self-labeling algorithm that produces meaningful text labels for the clusters. Through extensive experiments, we show that our pipeline works well on standard datasets such as CIFAR-10, CIFAR-100, and ImageNet-1k. It also extends to datasets without predefined labels, such as LAION-Aesthetics and WikiArts. We released the code in https://github.com/LeslieTrue/CPP.

Clustering is central to many data-driven application domains and has been studied extensively in terms of distance functions and grouping algorithms. Relatively little work has focused on learning representations for clustering. In this paper, we propose Deep Embedded Clustering (DEC), a method that simultaneously learns feature representations and cluster assignments using deep neural networks. DEC learns a mapping from the data space to a lower-dimensional feature space in which it iteratively optimizes a clustering objective. Our experimental evaluations on image and text corpora show significant improvement over state-of-the-art methods.

We introduce a novel class of sample-based explanations we term high-dimensional representers, that can be used to explain the predictions of a regularized high-dimensional model in terms of importance weights for each of the training samples. Our workhorse is a novel representer theorem for general regularized high-dimensional models, which decomposes the model prediction in terms of contributions from each of the training samples: with positive (negative) values corresponding to positive (negative) impact training samples to the model's prediction. We derive consequences for the canonical instances of ell_1 regularized sparse models, and nuclear norm regularized low-rank models. As a case study, we further investigate the application of low-rank models in the context of collaborative filtering, where we instantiate high-dimensional representers for specific popular classes of models. Finally, we study the empirical performance of our proposed methods on three real-world binary classification datasets and two recommender system datasets. We also showcase the utility of high-dimensional representers in explaining model recommendations.

Pre-training convolutional neural networks with weakly-supervised and self-supervised strategies is becoming increasingly popular for several computer vision tasks. However, due to the lack of strong discriminative signals, these learned representations may overfit to the pre-training objective (e.g., hashtag prediction) and not generalize well to downstream tasks. In this work, we present a simple strategy - ClusterFit (CF) to improve the robustness of the visual representations learned during pre-training. Given a dataset, we (a) cluster its features extracted from a pre-trained network using k-means and (b) re-train a new network from scratch on this dataset using cluster assignments as pseudo-labels. We empirically show that clustering helps reduce the pre-training task-specific information from the extracted features thereby minimizing overfitting to the same. Our approach is extensible to different pre-training frameworks -- weak- and self-supervised, modalities -- images and videos, and pre-training tasks -- object and action classification. Through extensive transfer learning experiments on 11 different target datasets of varied vocabularies and granularities, we show that ClusterFit significantly improves the representation quality compared to the state-of-the-art large-scale (millions / billions) weakly-supervised image and video models and self-supervised image models.

We study the data selection problem, whose aim is to select a small representative subset of data that can be used to efficiently train a machine learning model. We present a new data selection approach based on k-means clustering and sensitivity sampling. Assuming access to an embedding representation of the data with respect to which the model loss is H\"older continuous, our approach provably allows selecting a set of ``typical'' k + 1/varepsilon^2 elements whose average loss corresponds to the average loss of the whole dataset, up to a multiplicative (1pmvarepsilon) factor and an additive varepsilon lambda Phi_k, where Phi_k represents the k-means cost for the input embeddings and lambda is the H\"older constant. We furthermore demonstrate the performance and scalability of our approach on fine-tuning foundation models and show that it outperforms state-of-the-art methods. We also show how it can be applied on linear regression, leading to a new sampling strategy that surprisingly matches the performances of leverage score sampling, while being conceptually simpler and more scalable.

Self-supervised features are the cornerstone of modern machine learning systems. They are typically pre-trained on data collections whose construction and curation typically require extensive human effort. This manual process has some limitations similar to those encountered in supervised learning, e.g., the crowd-sourced selection of data is costly and time-consuming, preventing scaling the dataset size. In this work, we consider the problem of automatic curation of high-quality datasets for self-supervised pre-training. We posit that such datasets should be large, diverse and balanced, and propose a clustering-based approach for building ones satisfying all these criteria. Our method involves successive and hierarchical applications of k-means on a large and diverse data repository to obtain clusters that distribute uniformly among data concepts, followed by a hierarchical, balanced sampling step from these clusters. Extensive experiments on three different data domains including web-based images, satellite images and text show that features trained on our automatically curated datasets outperform those trained on uncurated data while being on par or better than ones trained on manually curated data.

We consider the problem of simultaneously clustering and learning a linear representation of data lying close to a union of low-dimensional manifolds, a fundamental task in machine learning and computer vision. When the manifolds are assumed to be linear subspaces, this reduces to the classical problem of subspace clustering, which has been studied extensively over the past two decades. Unfortunately, many real-world datasets such as natural images can not be well approximated by linear subspaces. On the other hand, numerous works have attempted to learn an appropriate transformation of the data, such that data is mapped from a union of general non-linear manifolds to a union of linear subspaces (with points from the same manifold being mapped to the same subspace). However, many existing works have limitations such as assuming knowledge of the membership of samples to clusters, requiring high sampling density, or being shown theoretically to learn trivial representations. In this paper, we propose to optimize the Maximal Coding Rate Reduction metric with respect to both the data representation and a novel doubly stochastic cluster membership, inspired by state-of-the-art subspace clustering results. We give a parameterization of such a representation and membership, allowing efficient mini-batching and one-shot initialization. Experiments on CIFAR-10, -20, -100, and TinyImageNet-200 datasets show that the proposed method is much more accurate and scalable than state-of-the-art deep clustering methods, and further learns a latent linear representation of the data.

Text clustering remains valuable in real-world applications where manual labeling is cost-prohibitive. It facilitates efficient organization and analysis of information by grouping similar texts based on their representations. However, implementing this approach necessitates fine-tuned embedders for downstream data and sophisticated similarity metrics. To address this issue, this study presents a novel framework for text clustering that effectively leverages the in-context learning capacity of Large Language Models (LLMs). Instead of fine-tuning embedders, we propose to transform the text clustering into a classification task via LLM. First, we prompt LLM to generate potential labels for a given dataset. Second, after integrating similar labels generated by the LLM, we prompt the LLM to assign the most appropriate label to each sample in the dataset. Our framework has been experimentally proven to achieve comparable or superior performance to state-of-the-art clustering methods that employ embeddings, without requiring complex fine-tuning or clustering algorithms. We make our code available to the public for utilization at https://anonymous.4open.science/r/Text-Clustering-via-LLM-E500.

Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captures the relevant geometric features of the data is a key step in many machine learning algorithms. Existing methods are restricted to specific kinds of metrics or small problem sizes because of the large number of metric constraints in such problems. In this paper, we provide an active set algorithm, Project and Forget, that uses Bregman projections, to solve metric constrained problems with many (possibly exponentially) inequality constraints. We provide a theoretical analysis of Project and Forget and prove that our algorithm converges to the global optimal solution and that the L_2 distance of the current iterate to the optimal solution decays asymptotically at an exponential rate. We demonstrate that using our method we can solve large problem instances of three types of metric constrained problems: general weight correlation clustering, metric nearness, and metric learning; in each case, out-performing the state of the art methods with respect to CPU times and problem sizes.

Clustering is a widely used unsupervised learning technique involving an intensive discrete optimization problem. Associative Memory models or AMs are differentiable neural networks defining a recursive dynamical system, which have been integrated with various deep learning architectures. We uncover a novel connection between the AM dynamics and the inherent discrete assignment necessary in clustering to propose a novel unconstrained continuous relaxation of the discrete clustering problem, enabling end-to-end differentiable clustering with AM, dubbed ClAM. Leveraging the pattern completion ability of AMs, we further develop a novel self-supervised clustering loss. Our evaluations on varied datasets demonstrate that ClAM benefits from the self-supervision, and significantly improves upon both the traditional Lloyd's k-means algorithm, and more recent continuous clustering relaxations (by upto 60% in terms of the Silhouette Coefficient).

Sparse autoencoders have recently produced dictionaries of high-dimensional vectors corresponding to the universe of concepts represented by large language models. We find that this concept universe has interesting structure at three levels: 1) The "atomic" small-scale structure contains "crystals" whose faces are parallelograms or trapezoids, generalizing well-known examples such as (man-woman-king-queen). We find that the quality of such parallelograms and associated function vectors improves greatly when projecting out global distractor directions such as word length, which is efficiently done with linear discriminant analysis. 2) The "brain" intermediate-scale structure has significant spatial modularity; for example, math and code features form a "lobe" akin to functional lobes seen in neural fMRI images. We quantify the spatial locality of these lobes with multiple metrics and find that clusters of co-occurring features, at coarse enough scale, also cluster together spatially far more than one would expect if feature geometry were random. 3) The "galaxy" scale large-scale structure of the feature point cloud is not isotropic, but instead has a power law of eigenvalues with steepest slope in middle layers. We also quantify how the clustering entropy depends on the layer.

Object-centric architectures usually apply a differentiable module to the entire feature map to decompose it into sets of entity representations called slots. Some of these methods structurally resemble clustering algorithms, where the cluster's center in latent space serves as a slot representation. Slot Attention is an example of such a method, acting as a learnable analog of the soft k-means algorithm. Our work employs a learnable clustering method based on the Gaussian Mixture Model. Unlike other approaches, we represent slots not only as centers of clusters but also incorporate information about the distance between clusters and assigned vectors, leading to more expressive slot representations. Our experiments demonstrate that using this approach instead of Slot Attention improves performance in object-centric scenarios, achieving state-of-the-art results in the set property prediction task.

We develop a novel theoretical framework for understating OT schemes respecting a class structure. For this purpose, we propose a convex OT program with a sum-of-norms regularization term, which provably recovers the underlying class structure under geometric assumptions. Furthermore, we derive an accelerated proximal algorithm with a closed-form projection and proximal operator scheme, thereby affording a more scalable algorithm for computing optimal transport plans. We provide a novel argument for the uniqueness of the optimum even in the absence of strong convexity. Our experiments show that the new regularizer not only results in a better preservation of the class structure in the data but also yields additional robustness to the data geometry, compared to previous regularizers.

Many clustering schemes are defined by optimizing an objective function defined on the partitions of the underlying set of a finite metric space. In this paper, we construct a framework for studying what happens when we instead impose various structural conditions on the clustering schemes, under the general heading of functoriality. Functoriality refers to the idea that one should be able to compare the results of clustering algorithms as one varies the data set, for example by adding points or by applying functions to it. We show that within this framework, one can prove a theorems analogous to one of J. Kleinberg, in which for example one obtains an existence and uniqueness theorem instead of a non-existence result. We obtain a full classification of all clustering schemes satisfying a condition we refer to as excisiveness. The classification can be changed by varying the notion of maps of finite metric spaces. The conditions occur naturally when one considers clustering as the statistical version of the geometric notion of connected components. By varying the degree of functoriality that one requires from the schemes it is possible to construct richer families of clustering schemes that exhibit sensitivity to density.

Clustering is a fundamental building block of modern statistical analysis pipelines. Fair clustering has seen much attention from the machine learning community in recent years. We are some of the first to study fairness in the context of hierarchical clustering, after the results of Ahmadian et al. from NeurIPS in 2020. We evaluate our results using Dasgupta's cost function, perhaps one of the most prevalent theoretical metrics for hierarchical clustering evaluation. Our work vastly improves the previous O(n^{5/6}polylog(n)) fair approximation for cost to a near polylogarithmic O(n^delta polylog(n)) fair approximation for any constant deltain(0,1). This result establishes a cost-fairness tradeoff and extends to broader fairness constraints than the previous work. We also show how to alter existing hierarchical clusterings to guarantee fairness and cluster balance across any level in the hierarchy.

Deep clustering, which learns representation and semantic clustering without labels information, poses a great challenge for deep learning-based approaches. Despite significant progress in recent years, most existing methods focus on uniformly distributed datasets, significantly limiting the practical applicability of their methods. In this paper, we first introduce a more practical problem setting named deep imbalanced clustering, where the underlying classes exhibit an imbalance distribution. To tackle this problem, we propose a novel pseudo-labeling-based learning framework. Our framework formulates pseudo-label generation as a progressive partial optimal transport problem, which progressively transports each sample to imbalanced clusters under prior distribution constraints, thus generating imbalance-aware pseudo-labels and learning from high-confident samples. In addition, we transform the initial formulation into an unbalanced optimal transport problem with augmented constraints, which can be solved efficiently by a fast matrix scaling algorithm. Experiments on various datasets, including a human-curated long-tailed CIFAR100, challenging ImageNet-R, and large-scale subsets of fine-grained iNaturalist2018 datasets, demonstrate the superiority of our method.

Deep clustering, which learns representation and semantic clustering without labels information, poses a great challenge for deep learning-based approaches. Despite significant progress in recent years, most existing methods focus on uniformly distributed datasets, significantly limiting the practical applicability of their methods. In this paper, we propose a more practical problem setting named deep imbalanced clustering, where the underlying classes exhibit an imbalance distribution. To address this challenge, we introduce a novel optimal transport-based pseudo-label learning framework. Our framework formulates pseudo-label generation as a Semantic-regularized Progressive Partial Optimal Transport (SP^2OT) problem, which progressively transports each sample to imbalanced clusters under several prior distribution and semantic relation constraints, thus generating high-quality and imbalance-aware pseudo-labels. To solve SP^2OT, we develop a Majorization-Minimization-based optimization algorithm. To be more precise, we employ the strategy of majorization to reformulate the SP^2OT problem into a Progressive Partial Optimal Transport problem, which can be transformed into an unbalanced optimal transport problem with augmented constraints and can be solved efficiently by a fast matrix scaling algorithm. Experiments on various datasets, including a human-curated long-tailed CIFAR100, challenging ImageNet-R, and large-scale subsets of fine-grained iNaturalist2018 datasets, demonstrate the superiority of our method.

We identify rare and visually distinctive galaxy populations by searching for structure within the learned representations of pretrained models. We show that these representations arrange galaxies by appearance in patterns beyond those needed to predict the pretraining labels. We design a clustering approach to isolate specific local patterns, revealing groups of galaxies with rare and scientifically-interesting morphologies.

We introduce fast algorithms for correlation clustering with respect to the Min Max objective that provide constant factor approximations on complete graphs. Our algorithms are the first purely combinatorial approximation algorithms for this problem. We construct a novel semi-metric on the set of vertices, which we call the correlation metric, that indicates to our clustering algorithms whether pairs of nodes should be in the same cluster. The paper demonstrates empirically that, compared to prior work, our algorithms sacrifice little in the objective quality to obtain significantly better run-time. Moreover, our algorithms scale to larger networks that are effectively intractable for known algorithms.

Classical clustering methods do not provide users with direct control of the clustering results, and the clustering results may not be consistent with the relevant criterion that a user has in mind. In this work, we present a new methodology for performing image clustering based on user-specified text criteria by leveraging modern vision-language models and large language models. We call our method Image Clustering Conditioned on Text Criteria (IC|TC), and it represents a different paradigm of image clustering. IC|TC requires a minimal and practical degree of human intervention and grants the user significant control over the clustering results in return. Our experiments show that IC|TC can effectively cluster images with various criteria, such as human action, physical location, or the person's mood, while significantly outperforming baselines.

The growing interest in machine learning problems over graphs with additional node information such as texts, images, or labels has popularized methods that require the costly operation of processing the entire graph. Yet, little effort has been made to the development of fast local methods (i.e. without accessing the entire graph) that extract useful information from such data. To that end, we propose a study of local graph clustering using noisy node labels as a proxy for additional node information. In this setting, nodes receive initial binary labels based on cluster affiliation: 1 if they belong to the target cluster and 0 otherwise. Subsequently, a fraction of these labels is flipped. We investigate the benefits of incorporating noisy labels for local graph clustering. By constructing a weighted graph with such labels, we study the performance of graph diffusion-based local clustering method on both the original and the weighted graphs. From a theoretical perspective, we consider recovering an unknown target cluster with a single seed node in a random graph with independent noisy node labels. We provide sufficient conditions on the label noise under which, with high probability, using diffusion in the weighted graph yields a more accurate recovery of the target cluster. This approach proves more effective than using the given labels alone or using diffusion in the label-free original graph. Empirically, we show that reliable node labels can be obtained with just a few samples from an attributed graph. Moreover, utilizing these labels via diffusion in the weighted graph leads to significantly better local clustering performance across several real-world datasets, improving F1 scores by up to 13%.

Smoothness and low dimensional structures play central roles in improving generalization and stability in learning and statistics. This work combines techniques from semi-infinite constrained learning and manifold regularization to learn representations that are globally smooth on a manifold. To do so, it shows that under typical conditions the problem of learning a Lipschitz continuous function on a manifold is equivalent to a dynamically weighted manifold regularization problem. This observation leads to a practical algorithm based on a weighted Laplacian penalty whose weights are adapted using stochastic gradient techniques. It is shown that under mild conditions, this method estimates the Lipschitz constant of the solution, learning a globally smooth solution as a byproduct. Experiments on real world data illustrate the advantages of the proposed method relative to existing alternatives.

Sparse Autoencoders (SAEs) have shown promise in improving the interpretability of neural network activations, but can learn features that are not features of the input, limiting their effectiveness. We propose Mutual Feature Regularization (MFR), a regularization technique for improving feature learning by encouraging SAEs trained in parallel to learn similar features. We motivate MFR by showing that features learned by multiple SAEs are more likely to correlate with features of the input. By training on synthetic data with known features of the input, we show that MFR can help SAEs learn those features, as we can directly compare the features learned by the SAE with the input features for the synthetic data. We then scale MFR to SAEs that are trained to denoise electroencephalography (EEG) data and SAEs that are trained to reconstruct GPT-2 Small activations. We show that MFR can improve the reconstruction loss of SAEs by up to 21.21\% on GPT-2 Small, and 6.67\% on EEG data. Our results suggest that the similarity between features learned by different SAEs can be leveraged to improve SAE training, thereby enhancing performance and the usefulness of SAEs for model interpretability.

Clustering aims to group unlabelled samples based on their similarities. It has become a significant tool for the analysis of high-dimensional data. However, most of the clustering methods merely generate pseudo labels and thus are unable to simultaneously present the similarities between different clusters and outliers. This paper proposes a new framework called High-dimensional Clustering onto Hamiltonian Cycle (HCHC) to solve the above problems. First, HCHC combines global structure with local structure in one objective function for deep clustering, improving the labels as relative probabilities, to mine the similarities between different clusters while keeping the local structure in each cluster. Then, the anchors of different clusters are sorted on the optimal Hamiltonian cycle generated by the cluster similarities and mapped on the circumference of a circle. Finally, a sample with a higher probability of a cluster will be mapped closer to the corresponding anchor. In this way, our framework allows us to appreciate three aspects visually and simultaneously - clusters (formed by samples with high probabilities), cluster similarities (represented as circular distances), and outliers (recognized as dots far away from all clusters). The experiments illustrate the superiority of HCHC.

Can we automatically group images into semantically meaningful clusters when ground-truth annotations are absent? The task of unsupervised image classification remains an important, and open challenge in computer vision. Several recent approaches have tried to tackle this problem in an end-to-end fashion. In this paper, we deviate from recent works, and advocate a two-step approach where feature learning and clustering are decoupled. First, a self-supervised task from representation learning is employed to obtain semantically meaningful features. Second, we use the obtained features as a prior in a learnable clustering approach. In doing so, we remove the ability for cluster learning to depend on low-level features, which is present in current end-to-end learning approaches. Experimental evaluation shows that we outperform state-of-the-art methods by large margins, in particular +26.6% on CIFAR10, +25.0% on CIFAR100-20 and +21.3% on STL10 in terms of classification accuracy. Furthermore, our method is the first to perform well on a large-scale dataset for image classification. In particular, we obtain promising results on ImageNet, and outperform several semi-supervised learning methods in the low-data regime without the use of any ground-truth annotations. The code is made publicly available at https://github.com/wvangansbeke/Unsupervised-Classification.

In this paper we propose a new approach to detect clusters in undirected graphs with attributed vertices. We incorporate structural and attribute similarities between the vertices in an augmented graph by creating additional vertices and edges as proposed in [1, 2]. The augmented graph is then embedded in a Euclidean space associated to its Laplacian and we cluster vertices via a modified K-means algorithm, using a new vector-valued distance in the embedding space. Main novelty of our method, which can be classified as an early fusion method, i.e., a method in which additional information on vertices are fused to the structure information before applying clustering, is the interpretation of attributes as new realizations of graph vertices, which can be dealt with as coordinate vectors in a related Euclidean space. This allows us to extend a scalable generalized spectral clustering procedure which substitutes graph Laplacian eigenvectors with some vectors, named algebraically smooth vectors, obtained by a linear-time complexity Algebraic MultiGrid (AMG) method. We discuss the performance of our proposed clustering method by comparison with recent literature approaches and public available results. Extensive experiments on different types of synthetic datasets and real-world attributed graphs show that our new algorithm, embedding attributes information in the clustering, outperforms structure-only-based methods, when the attributed network has an ambiguous structure. Furthermore, our new method largely outperforms the method which originally proposed the graph augmentation, showing that our embedding strategy and vector-valued distance are very effective in taking advantages from the augmented-graph representation.

We propose a graph clustering formulation based on multicut (a.k.a. weighted correlation clustering) on the complete graph. Our formulation does not need specification of the graph topology as in the original sparse formulation of multicut, making our approach simpler and potentially better performing. In contrast to unweighted correlation clustering we allow for a more expressive weighted cost structure. In dense multicut, the clustering objective is given in a factorized form as inner products of node feature vectors. This allows for an efficient formulation and inference in contrast to multicut/weighted correlation clustering, which has at least quadratic representation and computation complexity when working on the complete graph. We show how to rewrite classical greedy algorithms for multicut in our dense setting and how to modify them for greater efficiency and solution quality. In particular, our algorithms scale to graphs with tens of thousands of nodes. Empirical evidence on instance segmentation on Cityscapes and clustering of ImageNet datasets shows the merits of our approach.

Representations learned via self-supervised learning (SSL) can be susceptible to dimensional collapse, where the learned representation subspace is of extremely low dimensionality and thus fails to represent the full data distribution and modalities. Dimensional collapse also known as the "underfilling" phenomenon is one of the major causes of degraded performance on downstream tasks. Previous work has investigated the dimensional collapse problem of SSL at a global level. In this paper, we demonstrate that representations can span over high dimensional space globally, but collapse locally. To address this, we propose a method called local dimensionality regularization (LDReg). Our formulation is based on the derivation of the Fisher-Rao metric to compare and optimize local distance distributions at an asymptotically small radius for each data point. By increasing the local intrinsic dimensionality, we demonstrate through a range of experiments that LDReg improves the representation quality of SSL. The results also show that LDReg can regularize dimensionality at both local and global levels.

This work introduces a benchmark assessing the performance of clustering German text embeddings in different domains. This benchmark is driven by the increasing use of clustering neural text embeddings in tasks that require the grouping of texts (such as topic modeling) and the need for German resources in existing benchmarks. We provide an initial analysis for a range of pre-trained mono- and multilingual models evaluated on the outcome of different clustering algorithms. Results include strong performing mono- and multilingual models. Reducing the dimensions of embeddings can further improve clustering. Additionally, we conduct experiments with continued pre-training for German BERT models to estimate the benefits of this additional training. Our experiments suggest that significant performance improvements are possible for short text. All code and datasets are publicly available.

In this paper, we propose a recurrent framework for Joint Unsupervised LEarning (JULE) of deep representations and image clusters. In our framework, successive operations in a clustering algorithm are expressed as steps in a recurrent process, stacked on top of representations output by a Convolutional Neural Network (CNN). During training, image clusters and representations are updated jointly: image clustering is conducted in the forward pass, while representation learning in the backward pass. Our key idea behind this framework is that good representations are beneficial to image clustering and clustering results provide supervisory signals to representation learning. By integrating two processes into a single model with a unified weighted triplet loss and optimizing it end-to-end, we can obtain not only more powerful representations, but also more precise image clusters. Extensive experiments show that our method outperforms the state-of-the-art on image clustering across a variety of image datasets. Moreover, the learned representations generalize well when transferred to other tasks.

When training large flexible models, practitioners often rely on grid search to select hyperparameters that control over-fitting. This grid search has several disadvantages: the search is computationally expensive, requires carving out a validation set that reduces the available data for training, and requires users to specify candidate values. In this paper, we propose an alternative: directly learning regularization hyperparameters on the full training set via the evidence lower bound ("ELBo") objective from variational methods. For deep neural networks with millions of parameters, we recommend a modified ELBo that upweights the influence of the data likelihood relative to the prior. Our proposed technique overcomes all three disadvantages of grid search. In a case study on transfer learning of image classifiers, we show how our method reduces the 88+ hour grid search of past work to under 3 hours while delivering comparable accuracy. We further demonstrate how our approach enables efficient yet accurate approximations of Gaussian processes with learnable length-scale kernels.

We introduce a simple but effective unsupervised method for generating realistic and diverse images. We train a class-conditional GAN model without using manually annotated class labels. Instead, our model is conditional on labels automatically derived from clustering in the discriminator's feature space. Our clustering step automatically discovers diverse modes, and explicitly requires the generator to cover them. Experiments on standard mode collapse benchmarks show that our method outperforms several competing methods when addressing mode collapse. Our method also performs well on large-scale datasets such as ImageNet and Places365, improving both image diversity and standard quality metrics, compared to previous methods.

Imagine two high-dimensional clusters and a hyperplane separating them. Consider in particular the angle between: the direction joining the two clusters' centroids and the normal to the hyperplane. In linear classification, this angle depends on the level of L2 regularization used. Can you explain why?

Recently proposed Graph Neural Networks (GNNs) for vertex clustering are trained with an unsupervised minimum cut objective, approximated by a Spectral Clustering (SC) relaxation. However, the SC relaxation is loose and, while it offers a closed-form solution, it also yields overly smooth cluster assignments that poorly separate the vertices. In this paper, we propose a GNN model that computes cluster assignments by optimizing a tighter relaxation of the minimum cut based on graph total variation (GTV). The cluster assignments can be used directly to perform vertex clustering or to implement graph pooling in a graph classification framework. Our model consists of two core components: i) a message-passing layer that minimizes the ell_1 distance in the features of adjacent vertices, which is key to achieving sharp transitions between clusters; ii) an unsupervised loss function that minimizes the GTV of the cluster assignments while ensuring balanced partitions. Experimental results show that our model outperforms other GNNs for vertex clustering and graph classification.

We adapt previous research on category theory and topological unsupervised learning to develop a functorial perspective on manifold learning, also known as nonlinear dimensionality reduction. We first characterize manifold learning algorithms as functors that map pseudometric spaces to optimization objectives and that factor through hierarchical clustering functors. We then use this characterization to prove refinement bounds on manifold learning loss functions and construct a hierarchy of manifold learning algorithms based on their equivariants. We express several popular manifold learning algorithms as functors at different levels of this hierarchy, including Metric Multidimensional Scaling, IsoMap, and UMAP. Next, we use interleaving distance to study the stability of a broad class of manifold learning algorithms. We present bounds on how closely the embeddings these algorithms produce from noisy data approximate the embeddings they would learn from noiseless data. Finally, we use our framework to derive a set of novel manifold learning algorithms, which we experimentally demonstrate are competitive with the state of the art.

Combining clustering and representation learning is one of the most promising approaches for unsupervised learning of deep neural networks. However, doing so naively leads to ill posed learning problems with degenerate solutions. In this paper, we propose a novel and principled learning formulation that addresses these issues. The method is obtained by maximizing the information between labels and input data indices. We show that this criterion extends standard crossentropy minimization to an optimal transport problem, which we solve efficiently for millions of input images and thousands of labels using a fast variant of the Sinkhorn-Knopp algorithm. The resulting method is able to self-label visual data so as to train highly competitive image representations without manual labels. Our method achieves state of the art representation learning performance for AlexNet and ResNet-50 on SVHN, CIFAR-10, CIFAR-100 and ImageNet and yields the first self-supervised AlexNet that outperforms the supervised Pascal VOC detection baseline. Code and models are available.

Vibration-based condition monitoring systems are receiving increasing attention due to their ability to accurately identify different conditions by capturing dynamic features over a broad frequency range. However, there is little research on clustering approaches in vibration data and the resulting solutions are often optimized for a single data set. In this work, we present an extensive comparison of the clustering algorithms K-means clustering, OPTICS, and Gaussian mixture model clustering (GMM) applied to statistical features extracted from the time and frequency domains of vibration data sets. Furthermore, we investigate the influence of feature combinations, feature selection using principal component analysis (PCA), and the specified number of clusters on the performance of the clustering algorithms. We conducted this comparison in terms of a grid search using three different benchmark data sets. Our work showed that averaging (Mean, Median) and variance-based features (Standard Deviation, Interquartile Range) performed significantly better than shape-based features (Skewness, Kurtosis). In addition, K-means outperformed GMM slightly for these data sets, whereas OPTICS performed significantly worse. We were also able to show that feature combinations as well as PCA feature selection did not result in any significant performance improvements. With an increase in the specified number of clusters, clustering algorithms performed better, although there were some specific algorithmic restrictions.

Selecting an appropriate clustering method as well as an optimal number of clusters in road accident data is at times confusing and difficult. This paper analyzes shortcomings of different existing techniques applied to cluster accident-prone areas and recommends using Density-Based Spatial Clustering of Applications with Noise (DBSCAN) and Ordering Points To Identify the Clustering Structure (OPTICS) to overcome them. Comparative performance analysis based on real-life data on the recorded cases of road accidents in North Carolina also show more effectiveness and efficiency achieved by these algorithms.

Combinatorial inverse problems in high energy physics span enormous algorithmic challenges. This work presents a new deep learning driven clustering algorithm that utilizes a space-time non-local trainable graph constructor, a graph neural network, and a set transformer. The model is trained with loss functions at the graph node, edge and object level, including contrastive learning and meta-supervision. The algorithm can be applied to problems such as charged particle tracking, calorimetry, pile-up discrimination, jet physics, and beyond. We showcase the effectiveness of this cutting-edge AI approach through particle tracking simulations. The code is available online.

This paper offers a new perspective to ease the challenge of domain generalization, which involves maintaining robust results even in unseen environments. Our design focuses on the decision-making process in the final classifier layer. Specifically, we propose treating the element-wise contributions to the final results as the rationale for making a decision and representing the rationale for each sample as a matrix. For a well-generalized model, we suggest the rationale matrices for samples belonging to the same category should be similar, indicating the model relies on domain-invariant clues to make decisions, thereby ensuring robust results. To implement this idea, we introduce a rationale invariance loss as a simple regularization technique, requiring only a few lines of code. Our experiments demonstrate that the proposed approach achieves competitive results across various datasets, despite its simplicity. Code is available at https://github.com/liangchen527/RIDG.

In high dimension, low sample size (HDLSS) settings, classifiers based on Euclidean distances like the nearest neighbor classifier and the average distance classifier perform quite poorly if differences between locations of the underlying populations get masked by scale differences. To rectify this problem, several modifications of these classifiers have been proposed in the literature. However, existing methods are confined to location and scale differences only, and often fail to discriminate among populations differing outside of the first two moments. In this article, we propose some simple transformations of these classifiers resulting into improved performance even when the underlying populations have the same location and scale. We further propose a generalization of these classifiers based on the idea of grouping of variables. The high-dimensional behavior of the proposed classifiers is studied theoretically. Numerical experiments with a variety of simulated examples as well as an extensive analysis of real data sets exhibit advantages of the proposed methods.

Document clustering is a text mining technique used to provide better document search and browsing in digital libraries or online corpora. A lot of research has been done on biomedical document clustering that is based on using existing ontology. But, associations and co-occurrences of the medical concepts are not well represented by using ontology. In this research, a vector representation of concepts of diseases and similarity measurement between concepts are proposed. They identify the closest concepts of diseases in the context of a corpus. Each document is represented by using the vector space model. A weight scheme is proposed to consider both local content and associations between concepts. A Self-Organizing Map is used as document clustering algorithm. The vector projection and visualization features of SOM enable visualization and analysis of the clusters distributions and relationships on the two dimensional space. The experimental results show that the proposed document clustering framework generates meaningful clusters and facilitate visualization of the clusters based on the concepts of diseases.

Diffusion-based generative models have achieved remarkable success in various domains. It trains a shared model on denoising tasks that encompass different noise levels simultaneously, representing a form of multi-task learning (MTL). However, analyzing and improving diffusion models from an MTL perspective remains under-explored. In particular, MTL can sometimes lead to the well-known phenomenon of negative transfer, which results in the performance degradation of certain tasks due to conflicts between tasks. In this paper, we first aim to analyze diffusion training from an MTL standpoint, presenting two key observations: (O1) the task affinity between denoising tasks diminishes as the gap between noise levels widens, and (O2) negative transfer can arise even in diffusion training. Building upon these observations, we aim to enhance diffusion training by mitigating negative transfer. To achieve this, we propose leveraging existing MTL methods, but the presence of a huge number of denoising tasks makes this computationally expensive to calculate the necessary per-task loss or gradient. To address this challenge, we propose clustering the denoising tasks into small task clusters and applying MTL methods to them. Specifically, based on (O2), we employ interval clustering to enforce temporal proximity among denoising tasks within clusters. We show that interval clustering can be solved using dynamic programming, utilizing signal-to-noise ratio, timestep, and task affinity for clustering objectives. Through this, our approach addresses the issue of negative transfer in diffusion models by allowing for efficient computation of MTL methods. We validate the proposed clustering and its integration with MTL methods through various experiments, demonstrating improved sample quality of diffusion models. Our project page is available at https://gohyojun15.github.io/ANT_diffusion/{url}.

Visual clustering is a common perceptual task in scatterplots that supports diverse analytics tasks (e.g., cluster identification). However, even with the same scatterplot, the ways of perceiving clusters (i.e., conducting visual clustering) can differ due to the differences among individuals and ambiguous cluster boundaries. Although such perceptual variability casts doubt on the reliability of data analysis based on visual clustering, we lack a systematic way to efficiently assess this variability. In this research, we study perceptual variability in conducting visual clustering, which we call Cluster Ambiguity. To this end, we introduce CLAMS, a data-driven visual quality measure for automatically predicting cluster ambiguity in monochrome scatterplots. We first conduct a qualitative study to identify key factors that affect the visual separation of clusters (e.g., proximity or size difference between clusters). Based on study findings, we deploy a regression module that estimates the human-judged separability of two clusters. Then, CLAMS predicts cluster ambiguity by analyzing the aggregated results of all pairwise separability between clusters that are generated by the module. CLAMS outperforms widely-used clustering techniques in predicting ground truth cluster ambiguity. Meanwhile, CLAMS exhibits performance on par with human annotators. We conclude our work by presenting two applications for optimizing and benchmarking data mining techniques using CLAMS. The interactive demo of CLAMS is available at clusterambiguity.dev.

Contrastive Language Image Pre-training (CLIP) has recently demonstrated success across various tasks due to superior feature representation empowered by image-text contrastive learning. However, the instance discrimination method used by CLIP can hardly encode the semantic structure of training data. To handle this limitation, cluster discrimination has been proposed through iterative cluster assignment and classification. Nevertheless, most cluster discrimination approaches only define a single pseudo-label for each image, neglecting multi-label signals in the image. In this paper, we propose a novel Multi-Label Cluster Discrimination method named MLCD to enhance representation learning. In the clustering step, we first cluster the large-scale LAION-400M dataset into one million centers based on off-the-shelf embedding features. Considering that natural images frequently contain multiple visual objects or attributes, we select the multiple closest centers as auxiliary class labels. In the discrimination step, we design a novel multi-label classification loss, which elegantly separates losses from positive classes and negative classes, and alleviates ambiguity on decision boundary. We validate the proposed multi-label cluster discrimination method with experiments on different scales of models and pre-training datasets. Experimental results show that our method achieves state-of-the-art performance on multiple downstream tasks including linear probe, zero-shot classification, and image-text retrieval.

Masked Image Modeling (MIM) offers a promising approach to self-supervised representation learning, however existing MIM models still lag behind the state-of-the-art. In this paper, we systematically analyze target representations, loss functions, and architectures, to introduce CAPI - a novel pure-MIM framework that relies on the prediction of latent clusterings. Our approach leverages a clustering-based loss, which is stable to train, and exhibits promising scaling properties. Our ViT-L backbone, CAPI, achieves 83.8% accuracy on ImageNet and 32.1% mIoU on ADE20K with simple linear probes, substantially outperforming previous MIM methods and approaching the performance of the current state-of-the-art, DINOv2. We release all our code and models.

In this paper, we study two challenging problems in explainable AI (XAI) and data clustering. The first is how to directly design a neural network with inherent interpretability, rather than giving post-hoc explanations of a black-box model. The second is implementing discrete k-means with a differentiable neural network that embraces the advantages of parallel computing, online clustering, and clustering-favorable representation learning. To address these two challenges, we design a novel neural network, which is a differentiable reformulation of the vanilla k-means, called inTerpretable nEuraL cLustering (TELL). Our contributions are threefold. First, to the best of our knowledge, most existing XAI works focus on supervised learning paradigms. This work is one of the few XAI studies on unsupervised learning, in particular, data clustering. Second, TELL is an interpretable, or the so-called intrinsically explainable and transparent model. In contrast, most existing XAI studies resort to various means for understanding a black-box model with post-hoc explanations. Third, from the view of data clustering, TELL possesses many properties highly desired by k-means, including but not limited to online clustering, plug-and-play module, parallel computing, and provable convergence. Extensive experiments show that our method achieves superior performance comparing with 14 clustering approaches on three challenging data sets. The source code could be accessed at www.pengxi.me.

The higher-order correlation clustering problem is an expressive model, and recently, local search heuristics have been proposed for several applications. Certifying optimality, however, is NP-hard and practically hampered already by the complexity of the problem statement. Here, we focus on establishing partial optimality conditions for the special case of complete graphs and cubic objective functions. In addition, we define and implement algorithms for testing these conditions and examine their effect numerically, on two datasets.

Clustering has been a major research topic in the field of machine learning, one to which Deep Learning has recently been applied with significant success. However, an aspect of clustering that is not addressed by existing deep clustering methods, is that of efficiently producing multiple, diverse partitionings for a given dataset. This is particularly important, as a diverse set of base clusterings are necessary for consensus clustering, which has been found to produce better and more robust results than relying on a single clustering. To address this gap, we propose DivClust, a diversity controlling loss that can be incorporated into existing deep clustering frameworks to produce multiple clusterings with the desired degree of diversity. We conduct experiments with multiple datasets and deep clustering frameworks and show that: a) our method effectively controls diversity across frameworks and datasets with very small additional computational cost, b) the sets of clusterings learned by DivClust include solutions that significantly outperform single-clustering baselines, and c) using an off-the-shelf consensus clustering algorithm, DivClust produces consensus clustering solutions that consistently outperform single-clustering baselines, effectively improving the performance of the base deep clustering framework.

We study the ability of foundation models to learn representations for classification that are transferable to new, unseen classes. Recent results in the literature show that representations learned by a single classifier over many classes are competitive on few-shot learning problems with representations learned by special-purpose algorithms designed for such problems. In this paper we provide an explanation for this behavior based on the recently observed phenomenon that the features learned by overparameterized classification networks show an interesting clustering property, called neural collapse. We demonstrate both theoretically and empirically that neural collapse generalizes to new samples from the training classes, and -- more importantly -- to new classes as well, allowing foundation models to provide feature maps that work well in transfer learning and, specifically, in the few-shot setting.

We study differentially private (DP) algorithms for recovering clusters in well-clustered graphs, which are graphs whose vertex set can be partitioned into a small number of sets, each inducing a subgraph of high inner conductance and small outer conductance. Such graphs have widespread application as a benchmark in the theoretical analysis of spectral clustering. We provide an efficient (epsilon,delta)-DP algorithm tailored specifically for such graphs. Our algorithm draws inspiration from the recent work of Chen et al., who developed DP algorithms for recovery of stochastic block models in cases where the graph comprises exactly two nearly-balanced clusters. Our algorithm works for well-clustered graphs with k nearly-balanced clusters, and the misclassification ratio almost matches the one of the best-known non-private algorithms. We conduct experimental evaluations on datasets with known ground truth clusters to substantiate the prowess of our algorithm. We also show that any (pure) epsilon-DP algorithm would result in substantial error.

We present an accelerated algorithm for hierarchical density based clustering. Our new algorithm improves upon HDBSCAN*, which itself provided a significant qualitative improvement over the popular DBSCAN algorithm. The accelerated HDBSCAN* algorithm provides comparable performance to DBSCAN, while supporting variable density clusters, and eliminating the need for the difficult to tune distance scale parameter. This makes accelerated HDBSCAN* the default choice for density based clustering. Library available at: https://github.com/scikit-learn-contrib/hdbscan

Long-tailed recognition with imbalanced class distribution naturally emerges in practical machine learning applications. Existing methods such as data reweighing, resampling, and supervised contrastive learning enforce the class balance with a price of introducing imbalance between instances of head class and tail class, which may ignore the underlying rich semantic substructures of the former and exaggerate the biases in the latter. We overcome these drawbacks by a novel ``subclass-balancing contrastive learning (SBCL)'' approach that clusters each head class into multiple subclasses of similar sizes as the tail classes and enforce representations to capture the two-layer class hierarchy between the original classes and their subclasses. Since the clustering is conducted in the representation space and updated during the course of training, the subclass labels preserve the semantic substructures of head classes. Meanwhile, it does not overemphasize tail class samples, so each individual instance contribute to the representation learning equally. Hence, our method achieves both the instance- and subclass-balance, while the original class labels are also learned through contrastive learning among subclasses from different classes. We evaluate SBCL over a list of long-tailed benchmark datasets and it achieves the state-of-the-art performance. In addition, we present extensive analyses and ablation studies of SBCL to verify its advantages.

Diffusion-based manifold learning methods have proven useful in representation learning and dimensionality reduction of modern high dimensional, high throughput, noisy datasets. Such datasets are especially present in fields like biology and physics. While it is thought that these methods preserve underlying manifold structure of data by learning a proxy for geodesic distances, no specific theoretical links have been established. Here, we establish such a link via results in Riemannian geometry explicitly connecting heat diffusion to manifold distances. In this process, we also formulate a more general heat kernel based manifold embedding method that we call heat geodesic embeddings. This novel perspective makes clearer the choices available in manifold learning and denoising. Results show that our method outperforms existing state of the art in preserving ground truth manifold distances, and preserving cluster structure in toy datasets. We also showcase our method on single cell RNA-sequencing datasets with both continuum and cluster structure, where our method enables interpolation of withheld timepoints of data. Finally, we show that parameters of our more general method can be configured to give results similar to PHATE (a state-of-the-art diffusion based manifold learning method) as well as SNE (an attraction/repulsion neighborhood based method that forms the basis of t-SNE).

Designing recommendation systems with limited or no available training data remains a challenge. To that end, a new combinatorial optimization problem is formulated to generate optimized item selection for experimentation with the goal to shorten the time for collecting randomized training data. We first present an overview of the optimized item selection problem and a multi-level optimization framework to solve it. The approach integrates techniques from discrete optimization, unsupervised clustering, and latent text embeddings. We then discuss how to incorporate optimized item selection with active learning as part of randomized exploration in an ongoing fashion.

The mechanisms behind the success of multi-view self-supervised learning (MVSSL) are not yet fully understood. Contrastive MVSSL methods have been studied through the lens of InfoNCE, a lower bound of the Mutual Information (MI). However, the relation between other MVSSL methods and MI remains unclear. We consider a different lower bound on the MI consisting of an entropy and a reconstruction term (ER), and analyze the main MVSSL families through its lens. Through this ER bound, we show that clustering-based methods such as DeepCluster and SwAV maximize the MI. We also re-interpret the mechanisms of distillation-based approaches such as BYOL and DINO, showing that they explicitly maximize the reconstruction term and implicitly encourage a stable entropy, and we confirm this empirically. We show that replacing the objectives of common MVSSL methods with this ER bound achieves competitive performance, while making them stable when training with smaller batch sizes or smaller exponential moving average (EMA) coefficients. Github repo: https://github.com/apple/ml-entropy-reconstruction.

Galaxy clusters selected based on overdensities of galaxies in photometric surveys provide the largest cluster samples. Yet modeling the selection function of such samples is complicated by non-cluster members projected along the line of sight (projection effects) and the potential detection of unvirialized objects (contamination). We empirically constrain the magnitude of these effects by cross-matching galaxy clusters selected in the Dark Energy survey data with the \rdmpr, algorithm with significant detections in three South Pole Telescope surveys (SZ, pol-ECS, pol-500d). For matched clusters, we augment the \rdmpr,catalog by the SPT detection significance. For unmatched objects we use the SPT detection threshold as an upper limit on the SZe signature. Using a Bayesian population model applied to the collected multi-wavelength data, we explore various physically motivated models to describe the relationship between observed richness and halo mass. Our analysis reveals the limitations of a simple lognormal scatter model in describing the data. We rule out significant contamination by unvirialized objects at the high-richness end of the sample. While dedicated simulations offer a well-fitting calibration of projection effects, our findings suggest the presence of redshift-dependent trends that these simulations may not have captured. Our findings highlight that modeling the selection function of optically detected clusters remains a complicated challenge, requiring a combination of simulation and data-driven approaches.

Finding the mode of a high dimensional probability distribution D is a fundamental algorithmic problem in statistics and data analysis. There has been particular interest in efficient methods for solving the problem when D is represented as a mixture model or kernel density estimate, although few algorithmic results with worst-case approximation and runtime guarantees are known. In this work, we significantly generalize a result of (LeeLiMusco:2021) on mode approximation for Gaussian mixture models. We develop randomized dimensionality reduction methods for mixtures involving a broader class of kernels, including the popular logistic, sigmoid, and generalized Gaussian kernels. As in Lee et al.'s work, our dimensionality reduction results yield quasi-polynomial algorithms for mode finding with multiplicative accuracy (1-epsilon) for any epsilon > 0. Moreover, when combined with gradient descent, they yield efficient practical heuristics for the problem. In addition to our positive results, we prove a hardness result for box kernels, showing that there is no polynomial time algorithm for finding the mode of a kernel density estimate, unless P = NP. Obtaining similar hardness results for kernels used in practice (like Gaussian or logistic kernels) is an interesting future direction.

Currently, high-dimensional data is ubiquitous in data science, which necessitates the development of techniques to decompose and interpret such multidimensional (aka tensor) datasets. Finding a low dimensional representation of the data, that is, its inherent structure, is one of the approaches that can serve to understand the dynamics of low dimensional latent features hidden in the data. Nonnegative RESCAL is one such technique, particularly well suited to analyze self-relational data, such as dynamic networks found in international trade flows. Nonnegative RESCAL computes a low dimensional tensor representation by finding the latent space containing multiple modalities. Estimating the dimensionality of this latent space is crucial for extracting meaningful latent features. Here, to determine the dimensionality of the latent space with nonnegative RESCAL, we propose a latent dimension determination method which is based on clustering of the solutions of multiple realizations of nonnegative RESCAL decompositions. We demonstrate the performance of our model selection method on synthetic data and then we apply our method to decompose a network of international trade flows data from International Monetary Fund and validate the resulting features against empirical facts from economic literature.

Joint clustering and feature learning methods have shown remarkable performance in unsupervised representation learning. However, the training schedule alternating between feature clustering and network parameters update leads to unstable learning of visual representations. To overcome this challenge, we propose Online Deep Clustering (ODC) that performs clustering and network update simultaneously rather than alternatingly. Our key insight is that the cluster centroids should evolve steadily in keeping the classifier stably updated. Specifically, we design and maintain two dynamic memory modules, i.e., samples memory to store samples labels and features, and centroids memory for centroids evolution. We break down the abrupt global clustering into steady memory update and batch-wise label re-assignment. The process is integrated into network update iterations. In this way, labels and the network evolve shoulder-to-shoulder rather than alternatingly. Extensive experiments demonstrate that ODC stabilizes the training process and boosts the performance effectively. Code: https://github.com/open-mmlab/OpenSelfSup.

The recent integration of deep learning and pairwise similarity annotation-based constrained clustering -- i.e., deep constrained clustering (DCC) -- has proven effective for incorporating weak supervision into massive data clustering: Less than 1% of pair similarity annotations can often substantially enhance the clustering accuracy. However, beyond empirical successes, there is a lack of understanding of DCC. In addition, many DCC paradigms are sensitive to annotation noise, but performance-guaranteed noisy DCC methods have been largely elusive. This work first takes a deep look into a recently emerged logistic loss function of DCC, and characterizes its theoretical properties. Our result shows that the logistic DCC loss ensures the identifiability of data membership under reasonable conditions, which may shed light on its effectiveness in practice. Building upon this understanding, a new loss function based on geometric factor analysis is proposed to fend against noisy annotations. It is shown that even under unknown annotation confusions, the data membership can still be provably identified under our proposed learning criterion. The proposed approach is tested over multiple datasets to validate our claims.

We propose algorithms for approximate filtering and smoothing in high-dimensional Factorial hidden Markov models. The approximation involves discarding, in a principled way, likelihood factors according to a notion of locality in a factor graph associated with the emission distribution. This allows the exponential-in-dimension cost of exact filtering and smoothing to be avoided. We prove that the approximation accuracy, measured in a local total variation norm, is "dimension-free" in the sense that as the overall dimension of the model increases the error bounds we derive do not necessarily degrade. A key step in the analysis is to quantify the error introduced by localizing the likelihood function in a Bayes' rule update. The factorial structure of the likelihood function which we exploit arises naturally when data have known spatial or network structure. We demonstrate the new algorithms on synthetic examples and a London Underground passenger flow problem, where the factor graph is effectively given by the train network.

Recently, the retrieval models based on dense representations have been gradually applied in the first stage of the document retrieval tasks, showing better performance than traditional sparse vector space models. To obtain high efficiency, the basic structure of these models is Bi-encoder in most cases. However, this simple structure may cause serious information loss during the encoding of documents since the queries are agnostic. To address this problem, we design a method to mimic the queries on each of the documents by an iterative clustering process and represent the documents by multiple pseudo queries (i.e., the cluster centroids). To boost the retrieval process using approximate nearest neighbor search library, we also optimize the matching function with a two-step score calculation procedure. Experimental results on several popular ranking and QA datasets show that our model can achieve state-of-the-art results.

What do auto-encoders learn about the underlying data generating distribution? Recent work suggests that some auto-encoder variants do a good job of capturing the local manifold structure of data. This paper clarifies some of these previous observations by showing that minimizing a particular form of regularized reconstruction error yields a reconstruction function that locally characterizes the shape of the data generating density. We show that the auto-encoder captures the score (derivative of the log-density with respect to the input). It contradicts previous interpretations of reconstruction error as an energy function. Unlike previous results, the theorems provided here are completely generic and do not depend on the parametrization of the auto-encoder: they show what the auto-encoder would tend to if given enough capacity and examples. These results are for a contractive training criterion we show to be similar to the denoising auto-encoder training criterion with small corruption noise, but with contraction applied on the whole reconstruction function rather than just encoder. Similarly to score matching, one can consider the proposed training criterion as a convenient alternative to maximum likelihood because it does not involve a partition function. Finally, we show how an approximate Metropolis-Hastings MCMC can be setup to recover samples from the estimated distribution, and this is confirmed in sampling experiments.

Recent studies of large-scale contrastive pretraining in the text embedding domain show that using single-source minibatches, rather than mixed-source minibatches, can substantially improve overall model accuracy. In this work, we explore extending training data stratification beyond source granularity by leveraging a pretrained text embedding model and the classic k-means clustering algorithm to further split training data apart by the semantic clusters within each source. Experimentally, we observe a notable increase in NDCG@10 when pretraining a BERT-based text embedding model on query-passage pairs from the MSMARCO passage retrieval dataset. Additionally, we conceptually connect our clustering approach to both the Topic Aware Sampling (TAS) aspect of the TAS-B methodology and the nearest-neighbor-based hard-negative mining aspect of the ANCE methodology and discuss how this unified view motivates future lines of research on the organization of contrastive pretraining data.

Vector Quantization (VQ) is an appealing model compression method to obtain a tiny model with less accuracy loss. While methods to obtain better codebooks and codes under fixed clustering dimensionality have been extensively studied, optimizations of the vectors in favour of clustering performance are not carefully considered, especially via the reduction of vector dimensionality. This paper reports our recent progress on the combination of dimensionality compression and vector quantization, proposing a Low-Rank Representation Vector Quantization (LR^2VQ) method that outperforms previous VQ algorithms in various tasks and architectures. LR^2VQ joins low-rank representation with subvector clustering to construct a new kind of building block that is directly optimized through end-to-end training over the task loss. Our proposed design pattern introduces three hyper-parameters, the number of clusters k, the size of subvectors m and the clustering dimensionality d. In our method, the compression ratio could be directly controlled by m, and the final accuracy is solely determined by d. We recognize d as a trade-off between low-rank approximation error and clustering error and carry out both theoretical analysis and experimental observations that empower the estimation of the proper d before fine-tunning. With a proper d, we evaluate LR^2VQ with ResNet-18/ResNet-50 on ImageNet classification datasets, achieving 2.8\%/1.0\% top-1 accuracy improvements over the current state-of-the-art VQ-based compression algorithms with 43times/31times compression factor.

In recent years, concept-based approaches have emerged as some of the most promising explainability methods to help us interpret the decisions of Artificial Neural Networks (ANNs). These methods seek to discover intelligible visual 'concepts' buried within the complex patterns of ANN activations in two key steps: (1) concept extraction followed by (2) importance estimation. While these two steps are shared across methods, they all differ in their specific implementations. Here, we introduce a unifying theoretical framework that comprehensively defines and clarifies these two steps. This framework offers several advantages as it allows us: (i) to propose new evaluation metrics for comparing different concept extraction approaches; (ii) to leverage modern attribution methods and evaluation metrics to extend and systematically evaluate state-of-the-art concept-based approaches and importance estimation techniques; (iii) to derive theoretical guarantees regarding the optimality of such methods. We further leverage our framework to try to tackle a crucial question in explainability: how to efficiently identify clusters of data points that are classified based on a similar shared strategy. To illustrate these findings and to highlight the main strategies of a model, we introduce a visual representation called the strategic cluster graph. Finally, we present https://serre-lab.github.io/Lens, a dedicated website that offers a complete compilation of these visualizations for all classes of the ImageNet dataset.

Unsupervised semantic segmentation is a long-standing challenge in computer vision with great significance. Spectral clustering is a theoretically grounded solution to it where the spectral embeddings for pixels are computed to construct distinct clusters. Despite recent progress in enhancing spectral clustering with powerful pre-trained models, current approaches still suffer from inefficiencies in spectral decomposition and inflexibility in applying them to the test data. This work addresses these issues by casting spectral clustering as a parametric approach that employs neural network-based eigenfunctions to produce spectral embeddings. The outputs of the neural eigenfunctions are further restricted to discrete vectors that indicate clustering assignments directly. As a result, an end-to-end NN-based paradigm of spectral clustering emerges. In practice, the neural eigenfunctions are lightweight and take the features from pre-trained models as inputs, improving training efficiency and unleashing the potential of pre-trained models for dense prediction. We conduct extensive empirical studies to validate the effectiveness of our approach and observe significant performance gains over competitive baselines on Pascal Context, Cityscapes, and ADE20K benchmarks.

Small sample sizes are common in many disciplines, which necessitates pooling roughly similar datasets across multiple institutions to study weak but relevant associations between images and disease outcomes. Such data often manifest shift/imbalance in covariates (i.e., secondary non-imaging data). Controlling for such nuisance variables is common within standard statistical analysis, but the ideas do not directly apply to overparameterized models. Consequently, recent work has shown how strategies from invariant representation learning provides a meaningful starting point, but the current repertoire of methods is limited to accounting for shifts/imbalances in just a couple of covariates at a time. In this paper, we show how viewing this problem from the perspective of Category theory provides a simple and effective solution that completely avoids elaborate multi-stage training pipelines that would otherwise be needed. We show the effectiveness of this approach via extensive experiments on real datasets. Further, we discuss how this style of formulation offers a unified perspective on at least 5+ distinct problem settings, from self-supervised learning to matching problems in 3D reconstruction.

In this work, we study the challenge of providing human-understandable descriptions for failure modes in trained image classification models. Existing works address this problem by first identifying clusters (or directions) of incorrectly classified samples in a latent space and then aiming to provide human-understandable text descriptions for them. We observe that in some cases, describing text does not match well with identified failure modes, partially owing to the fact that shared interpretable attributes of failure modes may not be captured using clustering in the feature space. To improve on these shortcomings, we propose a novel approach that prioritizes interpretability in this problem: we start by obtaining human-understandable concepts (tags) of images in the dataset and then analyze the model's behavior based on the presence or absence of combinations of these tags. Our method also ensures that the tags describing a failure mode form a minimal set, avoiding redundant and noisy descriptions. Through several experiments on different datasets, we show that our method successfully identifies failure modes and generates high-quality text descriptions associated with them. These results highlight the importance of prioritizing interpretability in understanding model failures.

We study the approximability of an existing framework for clustering edge-colored hypergraphs, which is closely related to chromatic correlation clustering and is motivated by machine learning and data mining applications where the goal is to cluster a set of objects based on multiway interactions of different categories or types. We present improved approximation guarantees based on linear programming, and show they are tight by proving a matching integrality gap. Our results also include new approximation hardness results, a combinatorial 2-approximation whose runtime is linear in the hypergraph size, and several new connections to well-studied objectives such as vertex cover and hypergraph multiway cut.

Learning similarity is a key aspect in medical image analysis, particularly in recommendation systems or in uncovering the interpretation of anatomical data in images. Most existing methods learn such similarities in the embedding space over image sets using a single metric learner. Images, however, have a variety of object attributes such as color, shape, or artifacts. Encoding such attributes using a single metric learner is inadequate and may fail to generalize. Instead, multiple learners could focus on separate aspects of these attributes in subspaces of an overarching embedding. This, however, implies the number of learners to be found empirically for each new dataset. This work, Dynamic Subspace Learners, proposes to dynamically exploit multiple learners by removing the need of knowing apriori the number of learners and aggregating new subspace learners during training. Furthermore, the visual interpretability of such subspace learning is enforced by integrating an attention module into our method. This integrated attention mechanism provides a visual insight of discriminative image features that contribute to the clustering of image sets and a visual explanation of the embedding features. The benefits of our attention-based dynamic subspace learners are evaluated in the application of image clustering, image retrieval, and weakly supervised segmentation. Our method achieves competitive results with the performances of multiple learners baselines and significantly outperforms the classification network in terms of clustering and retrieval scores on three different public benchmark datasets. Moreover, our attention maps offer a proxy-labels, which improves the segmentation accuracy up to 15% in Dice scores when compared to state-of-the-art interpretation techniques.

Dense Retrieval (DR) has achieved state-of-the-art first-stage ranking effectiveness. However, the efficiency of most existing DR models is limited by the large memory cost of storing dense vectors and the time-consuming nearest neighbor search (NNS) in vector space. Therefore, we present RepCONC, a novel retrieval model that learns discrete Representations via CONstrained Clustering. RepCONC jointly trains dual-encoders and the Product Quantization (PQ) method to learn discrete document representations and enables fast approximate NNS with compact indexes. It models quantization as a constrained clustering process, which requires the document embeddings to be uniformly clustered around the quantization centroids and supports end-to-end optimization of the quantization method and dual-encoders. We theoretically demonstrate the importance of the uniform clustering constraint in RepCONC and derive an efficient approximate solution for constrained clustering by reducing it to an instance of the optimal transport problem. Besides constrained clustering, RepCONC further adopts a vector-based inverted file system (IVF) to support highly efficient vector search on CPUs. Extensive experiments on two popular ad-hoc retrieval benchmarks show that RepCONC achieves better ranking effectiveness than competitive vector quantization baselines under different compression ratio settings. It also substantially outperforms a wide range of existing retrieval models in terms of retrieval effectiveness, memory efficiency, and time efficiency.

Large scale recommender models find most relevant items from huge catalogs, and they play a critical role in modern search and recommendation systems. To model the input space with large-vocab categorical features, a typical recommender model learns a joint embedding space through neural networks for both queries and items from user feedback data. However, with millions to billions of items in the corpus, users tend to provide feedback for a very small set of them, causing a power-law distribution. This makes the feedback data for long-tail items extremely sparse. Inspired by the recent success in self-supervised representation learning research in both computer vision and natural language understanding, we propose a multi-task self-supervised learning (SSL) framework for large-scale item recommendations. The framework is designed to tackle the label sparsity problem by learning better latent relationship of item features. Specifically, SSL improves item representation learning as well as serving as additional regularization to improve generalization. Furthermore, we propose a novel data augmentation method that utilizes feature correlations within the proposed framework. We evaluate our framework using two real-world datasets with 500M and 1B training examples respectively. Our results demonstrate the effectiveness of SSL regularization and show its superior performance over the state-of-the-art regularization techniques. We also have already launched the proposed techniques to a web-scale commercial app-to-app recommendation system, with significant improvements top-tier business metrics demonstrated in A/B experiments on live traffic. Our online results also verify our hypothesis that our framework indeed improves model performance even more on slices that lack supervision.

Although deep neural networks achieve tremendous success on various classification tasks, the generalization ability drops sheer when training datasets exhibit long-tailed distributions. One of the reasons is that the learned representations (i.e. features) from the imbalanced datasets are less effective than those from balanced datasets. Specifically, the learned representation under class-balanced distribution will present the Neural Collapse (NC) phenomena. NC indicates the features from the same category are close to each other and from different categories are maximally distant, showing an optimal linear separable state of classification. However, the pattern differs on imbalanced datasets and is partially responsible for the reduced performance of the model. In this work, we propose two explicit feature regularization terms to learn high-quality representation for class-imbalanced data. With the proposed regularization, NC phenomena will appear under the class-imbalanced distribution, and the generalization ability can be significantly improved. Our method is easily implemented, highly effective, and can be plugged into most existing methods. The extensive experimental results on widely-used benchmarks show the effectiveness of our method

Nonlinear model order reduction has opened the door to parameter optimization and uncertainty quantification in complex physics problems governed by nonlinear equations. In particular, the computational cost of solving these equations can be reduced by means of local reduced-order bases. This article examines the benefits of a physics-informed cluster analysis for the construction of cluster-specific reduced-order bases. We illustrate that the choice of the dissimilarity measure for clustering is fundamental and highly affects the performances of the local reduced-order bases. It is shown that clustering with an angle-based dissimilarity on simulation data efficiently decreases the intra-cluster Kolmogorov N-width. Additionally, an a priori efficiency criterion is introduced to assess the relevance of a ROM-net, a methodology for the reduction of nonlinear physics problems introduced in our previous work in [T. Daniel, F. Casenave, N. Akkari, D. Ryckelynck, Model order reduction assisted by deep neural networks (ROM-net), Advanced Modeling and Simulation in Engineering Sciences 7 (16), 2020]. This criterion also provides engineers with a very practical method for ROM-nets' hyperparameters calibration under constrained computational costs for the training phase. On five different physics problems, our physics-informed clustering strategy significantly outperforms classic strategies for the construction of local reduced-order bases in terms of projection errors.

In the light of the COVID-19 pandemic, deep learning methods have been widely investigated in detecting COVID-19 from chest X-rays. However, a more pragmatic approach to applying AI methods to a medical diagnosis is designing a framework that facilitates human-machine interaction and expert decision making. Studies have shown that categorization can play an essential rule in accelerating real-world decision making. Inspired by descriptive document clustering, we propose a domain-independent explanatory clustering framework to group contextually related instances and support radiologists' decision making. While most descriptive clustering approaches employ domain-specific characteristics to form meaningful clusters, we focus on model-level explanation as a more general-purpose element of every learning process to achieve cluster homogeneity. We employ DeepSHAP to generate homogeneous clusters in terms of disease severity and describe the clusters using favorable and unfavorable saliency maps, which visualize the class discriminating regions of an image. These human-interpretable maps complement radiologist knowledge to investigate the whole cluster at once. Besides, as part of this study, we evaluate a model based on VGG-19, which can identify COVID and pneumonia cases with a positive predictive value of 95% and 97%, respectively, comparable to the recent explainable approaches for COVID diagnosis.

We consider the problem of estimating (diagonally dominant) M-matrices as precision matrices in Gaussian graphical models. These models exhibit intriguing properties, such as the existence of the maximum likelihood estimator with merely two observations for M-matrices lauritzen2019maximum,slawski2015estimation and even one observation for diagonally dominant M-matrices truell2021maximum. We propose an adaptive multiple-stage estimation method that refines the estimate by solving a weighted ell_1-regularized problem at each stage. Furthermore, we develop a unified framework based on the gradient projection method to solve the regularized problem, incorporating distinct projections to handle the constraints of M-matrices and diagonally dominant M-matrices. A theoretical analysis of the estimation error is provided. Our method outperforms state-of-the-art methods in precision matrix estimation and graph edge identification, as evidenced by synthetic and financial time-series data sets.

This paper introduces Least Volume-a simple yet effective regularization inspired by geometric intuition-that can reduce the necessary number of latent dimensions needed by an autoencoder without requiring any prior knowledge of the intrinsic dimensionality of the dataset. We show that the Lipschitz continuity of the decoder is the key to making it work, provide a proof that PCA is just a linear special case of it, and reveal that it has a similar PCA-like importance ordering effect when applied to nonlinear models. We demonstrate the intuition behind the regularization on some pedagogical toy problems, and its effectiveness on several benchmark problems, including MNIST, CIFAR-10 and CelebA.

Node clustering is a powerful tool in the analysis of networks. We introduce a graph neural network framework, named DIGRAC, to obtain node embeddings for directed networks in a self-supervised manner, including a novel probabilistic imbalance loss, which can be used for network clustering. Here, we propose directed flow imbalance measures, which are tightly related to directionality, to reveal clusters in the network even when there is no density difference between clusters. In contrast to standard approaches in the literature, in this paper, directionality is not treated as a nuisance, but rather contains the main signal. DIGRAC optimizes directed flow imbalance for clustering without requiring label supervision, unlike existing graph neural network methods, and can naturally incorporate node features, unlike existing spectral methods. Extensive experimental results on synthetic data, in the form of directed stochastic block models, and real-world data at different scales, demonstrate that our method, based on flow imbalance, attains state-of-the-art results on directed graph clustering when compared against 10 state-of-the-art methods from the literature, for a wide range of noise and sparsity levels, graph structures, and topologies, and even outperforms supervised methods.

Graph measures that express closeness or distance between nodes can be employed for graph nodes clustering using metric clustering algorithms. There are numerous measures applicable to this task, and which one performs better is an open question. We study the performance of 25 graph measures on generated graphs with different parameters. While usually measure comparisons are limited to general measure ranking on a particular dataset, we aim to explore the performance of various measures depending on graph features. Using an LFR graph generator, we create a dataset of 11780 graphs covering the whole LFR parameter space. For each graph, we assess the quality of clustering with k-means algorithm for each considered measure. Based on this, we determine the best measure for each area of the parameter space. We find that the parameter space consists of distinct zones where one particular measure is the best. We analyze the geometry of the resulting zones and describe it with simple criteria. Given particular graph parameters, this allows us to recommend a particular measure to use for clustering.

In representation learning, uniformity refers to the uniform feature distribution in the latent space (i.e., unit hypersphere). Previous work has shown that improving uniformity contributes to the learning of under-represented classes. However, most of the previous work focused on classification; the representation space of imbalanced regression remains unexplored. Classification-based methods are not suitable for regression tasks because they cluster features into distinct groups without considering the continuous and ordered nature essential for regression. In a geometric aspect, we uniquely focus on ensuring uniformity in the latent space for imbalanced regression through two key losses: enveloping and homogeneity. The enveloping loss encourages the induced trace to uniformly occupy the surface of a hypersphere, while the homogeneity loss ensures smoothness, with representations evenly spaced at consistent intervals. Our method integrates these geometric principles into the data representations via a Surrogate-driven Representation Learning (SRL) framework. Experiments with real-world regression and operator learning tasks highlight the importance of uniformity in imbalanced regression and validate the efficacy of our geometry-based loss functions.

Contrastive learning has recently achieved remarkable success in many domains including graphs. However contrastive loss, especially for graphs, requires a large number of negative samples which is unscalable and computationally prohibitive with a quadratic time complexity. Sub-sampling is not optimal and incorrect negative sampling leads to sampling bias. In this work, we propose a meta-node based approximation technique that can (a) proxy all negative combinations (b) in quadratic cluster size time complexity, (c) at graph level, not node level, and (d) exploit graph sparsity. By replacing node-pairs with additive cluster-pairs, we compute the negatives in cluster-time at graph level. The resulting Proxy approximated meta-node Contrastive (PamC) loss, based on simple optimized GPU operations, captures the full set of negatives, yet is efficient with a linear time complexity. By avoiding sampling, we effectively eliminate sample bias. We meet the criterion for larger number of samples, thus achieving block-contrastiveness, which is proven to outperform pair-wise losses. We use learnt soft cluster assignments for the meta-node constriction, and avoid possible heterophily and noise added during edge creation. Theoretically, we show that real world graphs easily satisfy conditions necessary for our approximation. Empirically, we show promising accuracy gains over state-of-the-art graph clustering on 6 benchmarks. Importantly, we gain substantially in efficiency; up to 3x in training time, 1.8x in inference time and over 5x in GPU memory reduction.

Google users have different intents from their queries such as acquiring information, buying products, comparing or simulating services, looking for products, and so on. Understanding the right intention of users helps to provide i) better content on web pages from the Search Engine Optimization (SEO) perspective and ii) more user-satisfying results from the search engine perspective. In this study, we aim to identify the user query's intent by taking advantage of Google results and machine learning methods. Our proposed approach is a clustering model that exploits some features to detect query's intent. A list of keywords extracted from the clustered queries is used to identify the intent of a new given query. Comparing the clustering results with the intents predicted by filtered keywords show the efficiency of the extracted keywords for detecting intents.

We tackle the novel class discovery in point cloud segmentation, which discovers novel classes based on the semantic knowledge of seen classes. Existing work proposes an online point-wise clustering method with a simplified equal class-size constraint on the novel classes to avoid degenerate solutions. However, the inherent imbalanced distribution of novel classes in point clouds typically violates the equal class-size constraint. Moreover, point-wise clustering ignores the rich spatial context information of objects, which results in less expressive representation for semantic segmentation. To address the above challenges, we propose a novel self-labeling strategy that adaptively generates high-quality pseudo-labels for imbalanced classes during model training. In addition, we develop a dual-level representation that incorporates regional consistency into the point-level classifier learning, reducing noise in generated segmentation. Finally, we conduct extensive experiments on two widely used datasets, SemanticKITTI and SemanticPOSS, and the results show our method outperforms the state of the art by a large margin.

Dimensionality reduction methods are unsupervised approaches which learn low-dimensional spaces where some properties of the initial space, typically the notion of "neighborhood", are preserved. Such methods usually require propagation on large k-NN graphs or complicated optimization solvers. On the other hand, self-supervised learning approaches, typically used to learn representations from scratch, rely on simple and more scalable frameworks for learning. In this paper, we propose TLDR, a dimensionality reduction method for generic input spaces that is porting the recent self-supervised learning framework of Zbontar et al. (2021) to the specific task of dimensionality reduction, over arbitrary representations. We propose to use nearest neighbors to build pairs from a training set and a redundancy reduction loss to learn an encoder that produces representations invariant across such pairs. TLDR is a method that is simple, easy to train, and of broad applicability; it consists of an offline nearest neighbor computation step that can be highly approximated, and a straightforward learning process. Aiming for scalability, we focus on improving linear dimensionality reduction, and show consistent gains on image and document retrieval tasks, e.g. gaining +4% mAP over PCA on ROxford for GeM- AP, improving the performance of DINO on ImageNet or retaining it with a 10x compression.

Metric space magnitude, an active field of research in algebraic topology, is a scalar quantity that summarizes the effective number of distinct points that live in a general metric space. The {\em weighting vector} is a closely-related concept that captures, in a nontrivial way, much of the underlying geometry of the original metric space. Recent work has demonstrated that when the metric space is Euclidean, the weighting vector serves as an effective tool for boundary detection. We recast this result and show the weighting vector may be viewed as a solution to a kernelized SVM. As one consequence, we apply this new insight to the task of outlier detection, and we demonstrate performance that is competitive or exceeds performance of state-of-the-art techniques on benchmark data sets. Under mild assumptions, we show the weighting vector, which has computational cost of matrix inversion, can be efficiently approximated in linear time. We show how nearest neighbor methods can approximate solutions to the minimization problems defined by SVMs.

Multiview clustering (MVC) aims to reveal the underlying structure of multiview data by categorizing data samples into clusters. Deep learning-based methods exhibit strong feature learning capabilities on large-scale datasets. For most existing deep MVC methods, exploring the invariant representations of multiple views is still an intractable problem. In this paper, we propose a cross-view contrastive learning (CVCL) method that learns view-invariant representations and produces clustering results by contrasting the cluster assignments among multiple views. Specifically, we first employ deep autoencoders to extract view-dependent features in the pretraining stage. Then, a cluster-level CVCL strategy is presented to explore consistent semantic label information among the multiple views in the fine-tuning stage. Thus, the proposed CVCL method is able to produce more discriminative cluster assignments by virtue of this learning strategy. Moreover, we provide a theoretical analysis of soft cluster assignment alignment. Extensive experimental results obtained on several datasets demonstrate that the proposed CVCL method outperforms several state-of-the-art approaches.

t-distributed Stochastic Neighborhood Embedding (t-SNE) is a method for dimensionality reduction and visualization that has become widely popular in recent years. Efficient implementations of t-SNE are available, but they scale poorly to datasets with hundreds of thousands to millions of high dimensional data-points. We present Fast Fourier Transform-accelerated Interpolation-based t-SNE (FIt-SNE), which dramatically accelerates the computation of t-SNE. The most time-consuming step of t-SNE is a convolution that we accelerate by interpolating onto an equispaced grid and subsequently using the fast Fourier transform to perform the convolution. We also optimize the computation of input similarities in high dimensions using multi-threaded approximate nearest neighbors. We further present a modification to t-SNE called "late exaggeration," which allows for easier identification of clusters in t-SNE embeddings. Finally, for datasets that cannot be loaded into the memory, we present out-of-core randomized principal component analysis (oocPCA), so that the top principal components of a dataset can be computed without ever fully loading the matrix, hence allowing for t-SNE of large datasets to be computed on resource-limited machines.

Despite their remarkable effectiveness and broad application, the drivers of success underlying ensembles of trees are still not fully understood. In this paper, we highlight how interpreting tree ensembles as adaptive and self-regularizing smoothers can provide new intuition and deeper insight to this topic. We use this perspective to show that, when studied as smoothers, randomized tree ensembles not only make predictions that are quantifiably more smooth than the predictions of the individual trees they consist of, but also further regulate their smoothness at test-time based on the dissimilarity between testing and training inputs. First, we use this insight to revisit, refine and reconcile two recent explanations of forest success by providing a new way of quantifying the conjectured behaviors of tree ensembles objectively by measuring the effective degree of smoothing they imply. Then, we move beyond existing explanations for the mechanisms by which tree ensembles improve upon individual trees and challenge the popular wisdom that the superior performance of forests should be understood as a consequence of variance reduction alone. We argue that the current high-level dichotomy into bias- and variance-reduction prevalent in statistics is insufficient to understand tree ensembles -- because the prevailing definition of bias does not capture differences in the expressivity of the hypothesis classes formed by trees and forests. Instead, we show that forests can improve upon trees by three distinct mechanisms that are usually implicitly entangled. In particular, we demonstrate that the smoothing effect of ensembling can reduce variance in predictions due to noise in outcome generation, reduce variability in the quality of the learned function given fixed input data and reduce potential bias in learnable functions by enriching the available hypothesis space.

We present a novel approach for traffic forecasting in urban traffic scenarios using a combination of spectral graph analysis and deep learning. We predict both the low-level information (future trajectories) as well as the high-level information (road-agent behavior) from the extracted trajectory of each road-agent. Our formulation represents the proximity between the road agents using a weighted dynamic geometric graph (DGG). We use a two-stream graph-LSTM network to perform traffic forecasting using these weighted DGGs. The first stream predicts the spatial coordinates of road-agents, while the second stream predicts whether a road-agent is going to exhibit overspeeding, underspeeding, or neutral behavior by modeling spatial interactions between road-agents. Additionally, we propose a new regularization algorithm based on spectral clustering to reduce the error margin in long-term prediction (3-5 seconds) and improve the accuracy of the predicted trajectories. Moreover, we prove a theoretical upper bound on the regularized prediction error. We evaluate our approach on the Argoverse, Lyft, Apolloscape, and NGSIM datasets and highlight the benefits over prior trajectory prediction methods. In practice, our approach reduces the average prediction error by approximately 75% over prior algorithms and achieves a weighted average accuracy of 91.2% for behavior prediction. Additionally, our spectral regularization improves long-term prediction by up to 70%.

In practical scenarios, the effectiveness of sequential recommendation systems is hindered by the user cold-start problem, which arises due to limited interactions for accurately determining user preferences. Previous studies have attempted to address this issue by combining meta-learning with user and item-side information. However, these approaches face inherent challenges in modeling user preference dynamics, particularly for "minor users" who exhibit distinct preferences compared to more common or "major users." To overcome these limitations, we present a novel approach called ClusterSeq, a Meta-Learning Clustering-Based Sequential Recommender System. ClusterSeq leverages dynamic information in the user sequence to enhance item prediction accuracy, even in the absence of side information. This model preserves the preferences of minor users without being overshadowed by major users, and it capitalizes on the collective knowledge of users within the same cluster. Extensive experiments conducted on various benchmark datasets validate the effectiveness of ClusterSeq. Empirical results consistently demonstrate that ClusterSeq outperforms several state-of-the-art meta-learning recommenders. Notably, compared to existing meta-learning methods, our proposed approach achieves a substantial improvement of 16-39% in Mean Reciprocal Rank (MRR).

Anti-Money Laundering (AML) is a crucial task in ensuring the integrity of financial systems. One keychallenge in AML is identifying high-risk groups based on their behavior. Unsupervised learning, particularly clustering, is a promising solution for this task. However, the use of hundreds of features todescribe behavior results in a highdimensional dataset that negatively impacts clustering performance.In this paper, we investigate the effectiveness of combining clustering method agglomerative hierarchicalclustering with four dimensionality reduction techniques -Independent Component Analysis (ICA), andKernel Principal Component Analysis (KPCA), Singular Value Decomposition (SVD), Locality Preserving Projections (LPP)- to overcome the issue of high-dimensionality in AML data and improve clusteringresults. This study aims to provide insights into the most effective way of reducing the dimensionality ofAML data and enhance the accuracy of clustering-based AML systems. The experimental results demonstrate that KPCA outperforms other dimension reduction techniques when combined with agglomerativehierarchical clustering. This superiority is observed in the majority of situations, as confirmed by threedistinct validation indices.

Supervised machine learning methods for geological mapping via remote sensing face limitations due to the scarcity of accurately labelled training data that can be addressed by unsupervised learning, such as dimensionality reduction and clustering. Dimensionality reduction methods have the potential to play a crucial role in improving the accuracy of geological maps. Although conventional dimensionality reduction methods may struggle with nonlinear data, unsupervised deep learning models such as autoencoders can model non-linear relationships. Stacked autoencoders feature multiple interconnected layers to capture hierarchical data representations useful for remote sensing data. We present an unsupervised machine learning-based framework for processing remote sensing data using stacked autoencoders for dimensionality reduction and k-means clustering for mapping geological units. We use Landsat 8, ASTER, and Sentinel-2 datasets to evaluate the framework for geological mapping of the Mutawintji region in Western New South Wales, Australia. We also compare stacked autoencoders with principal component analysis (PCA) and canonical autoencoders. Our results reveal that the framework produces accurate and interpretable geological maps, efficiently discriminating rock units. The results reveal that the combination of stacked autoencoders with Sentinel-2 data yields the best performance accuracy when compared to other combinations. We find that stacked autoencoders enable better extraction of complex and hierarchical representations of the input data when compared to canonical autoencoders and PCA. We also find that the generated maps align with prior geological knowledge of the study area while providing novel insights into geological structures.

What sorts of structure might enable a learner to discover classes from unlabeled data? Traditional approaches rely on feature-space similarity and heroic assumptions on the data. In this paper, we introduce unsupervised learning under Latent Label Shift (LLS), where we have access to unlabeled data from multiple domains such that the label marginals p_d(y) can shift across domains but the class conditionals p(x|y) do not. This work instantiates a new principle for identifying classes: elements that shift together group together. For finite input spaces, we establish an isomorphism between LLS and topic modeling: inputs correspond to words, domains to documents, and labels to topics. Addressing continuous data, we prove that when each label's support contains a separable region, analogous to an anchor word, oracle access to p(d|x) suffices to identify p_d(y) and p_d(y|x) up to permutation. Thus motivated, we introduce a practical algorithm that leverages domain-discriminative models as follows: (i) push examples through domain discriminator p(d|x); (ii) discretize the data by clustering examples in p(d|x) space; (iii) perform non-negative matrix factorization on the discrete data; (iv) combine the recovered p(y|d) with the discriminator outputs p(d|x) to compute p_d(y|x) ; forall d. With semi-synthetic experiments, we show that our algorithm can leverage domain information to improve upon competitive unsupervised classification methods. We reveal a failure mode of standard unsupervised classification methods when feature-space similarity does not indicate true groupings, and show empirically that our method better handles this case. Our results establish a deep connection between distribution shift and topic modeling, opening promising lines for future work.

Contrastive learning (CL) has emerged as a powerful technique for representation learning, with or without label supervision. However, supervised CL is prone to collapsing representations of subclasses within a class by not capturing all their features, and unsupervised CL may suppress harder class-relevant features by focusing on learning easy class-irrelevant features; both significantly compromise representation quality. Yet, there is no theoretical understanding of class collapse or feature suppression at test time. We provide the first unified theoretically rigorous framework to determine which features are learnt by CL. Our analysis indicate that, perhaps surprisingly, bias of (stochastic) gradient descent towards finding simpler solutions is a key factor in collapsing subclass representations and suppressing harder class-relevant features. Moreover, we present increasing embedding dimensionality and improving the quality of data augmentations as two theoretically motivated solutions to {feature suppression}. We also provide the first theoretical explanation for why employing supervised and unsupervised CL together yields higher-quality representations, even when using commonly-used stochastic gradient methods.

Deep neural networks exploiting millions of parameters are nowadays the norm in deep learning applications. This is a potential issue because of the great amount of computational resources needed for training, and of the possible loss of generalization performance of overparametrized networks. We propose in this paper a method for learning sparse neural topologies via a regularization technique which identifies non relevant weights and selectively shrinks their norm, while performing a classic update for relevant ones. This technique, which is an improvement of classical weight decay, is based on the definition of a regularization term which can be added to any loss functional regardless of its form, resulting in a unified general framework exploitable in many different contexts. The actual elimination of parameters identified as irrelevant is handled by an iterative pruning algorithm. We tested the proposed technique on different image classification and Natural language generation tasks, obtaining results on par or better then competitors in terms of sparsity and metrics, while achieving strong models compression.

Unsupervised semantic segmentation aims to achieve high-quality semantic grouping without human-labeled annotations. With the advent of self-supervised pre-training, various frameworks utilize the pre-trained features to train prediction heads for unsupervised dense prediction. However, a significant challenge in this unsupervised setup is determining the appropriate level of clustering required for segmenting concepts. To address it, we propose a novel framework, CAusal Unsupervised Semantic sEgmentation (CAUSE), which leverages insights from causal inference. Specifically, we bridge intervention-oriented approach (i.e., frontdoor adjustment) to define suitable two-step tasks for unsupervised prediction. The first step involves constructing a concept clusterbook as a mediator, which represents possible concept prototypes at different levels of granularity in a discretized form. Then, the mediator establishes an explicit link to the subsequent concept-wise self-supervised learning for pixel-level grouping. Through extensive experiments and analyses on various datasets, we corroborate the effectiveness of CAUSE and achieve state-of-the-art performance in unsupervised semantic segmentation.

We introduce ensembles within score-based sampling methods to develop gradient-free approximate sampling techniques that leverage the collective dynamics of particle ensembles to compute approximate reverse diffusion drifts. We introduce the underlying methodology, emphasizing its relationship with generative diffusion models and the previously introduced F\"ollmer sampler. We demonstrate the efficacy of ensemble strategies through various examples, ranging from low- to medium-dimensionality sampling problems, including multi-modal and highly non-Gaussian probability distributions, and provide comparisons to traditional methods like NUTS. Our findings highlight the potential of ensemble strategies for modeling complex probability distributions in situations where gradients are unavailable. Finally, we showcase its application in the context of Bayesian inversion problems within the geophysical sciences.

We explore the problem of generating minority samples using diffusion models. The minority samples are instances that lie on low-density regions of a data manifold. Generating a sufficient number of such minority instances is important, since they often contain some unique attributes of the data. However, the conventional generation process of the diffusion models mostly yields majority samples (that lie on high-density regions of the manifold) due to their high likelihoods, making themselves ineffective and time-consuming for the minority generating task. In this work, we present a novel framework that can make the generation process of the diffusion models focus on the minority samples. We first highlight that Tweedie's denoising formula yields favorable results for majority samples. The observation motivates us to introduce a metric that describes the uniqueness of a given sample. To address the inherent preference of the diffusion models w.r.t. the majority samples, we further develop minority guidance, a sampling technique that can guide the generation process toward regions with desired likelihood levels. Experiments on benchmark real datasets demonstrate that our minority guidance can greatly improve the capability of generating high-quality minority samples over existing generative samplers. We showcase that the performance benefit of our framework persists even in demanding real-world scenarios such as medical imaging, further underscoring the practical significance of our work. Code is available at https://github.com/soobin-um/minority-guidance.

Loss of plasticity is a phenomenon where neural networks become more difficult to train during the course of learning. Continual learning algorithms seek to mitigate this effect by sustaining good predictive performance while maintaining network trainability. We develop new techniques for improving continual learning by first reconsidering how initialization can ensure trainability during early phases of learning. From this perspective, we derive new regularization strategies for continual learning that ensure beneficial initialization properties are better maintained throughout training. In particular, we investigate two new regularization techniques for continual learning: (i) Wasserstein regularization toward the initial weight distribution, which is less restrictive than regularizing toward initial weights; and (ii) regularizing weight matrix singular values, which directly ensures gradient diversity is maintained throughout training. We present an experimental analysis that shows these alternative regularizers can improve continual learning performance across a range of supervised learning tasks and model architectures. The alternative regularizers prove to be less sensitive to hyperparameters while demonstrating better training in individual tasks, sustaining trainability as new tasks arrive, and achieving better generalization performance.

Clustering non-Euclidean data is difficult, and one of the most used algorithms besides hierarchical clustering is the popular algorithm Partitioning Around Medoids (PAM), also simply referred to as k-medoids clustering. In Euclidean geometry the mean-as used in k-means-is a good estimator for the cluster center, but this does not exist for arbitrary dissimilarities. PAM uses the medoid instead, the object with the smallest dissimilarity to all others in the cluster. This notion of centrality can be used with any (dis-)similarity, and thus is of high relevance to many domains and applications. A key issue with PAM is its high run time cost. We propose modifications to the PAM algorithm that achieve an O(k)-fold speedup in the second ("SWAP") phase of the algorithm, but will still find the same results as the original PAM algorithm. If we relax the choice of swaps performed (while retaining comparable quality), we can further accelerate the algorithm by eagerly performing additional swaps in each iteration. With the substantially faster SWAP, we can now explore faster initialization strategies, because (i) the classic ("BUILD") initialization now becomes the bottleneck, and (ii) our swap is fast enough to compensate for worse starting conditions. We also show how the CLARA and CLARANS algorithms benefit from the proposed modifications. While we do not study the parallelization of our approach in this work, it can easily be combined with earlier approaches to use PAM and CLARA on big data (some of which use PAM as a subroutine, hence can immediately benefit from these improvements), where the performance with high k becomes increasingly important. In experiments on real data with k=100,200, we observed a 458x respectively 1191x speedup compared to the original PAM SWAP algorithm, making PAM applicable to larger data sets, and in particular to higher k.

Despite the widespread application of latent factor analysis, existing methods suffer from the following weaknesses: requiring the number of factors to be known, lack of theoretical guarantees for learning the model structure, and nonidentifiability of the parameters due to rotation invariance properties of the likelihood. We address these concerns by proposing a fast correlation thresholding (CT) algorithm that simultaneously learns the number of latent factors and a rotationally identifiable model structure. Our novel approach translates this structure learning problem into the search for so-called independent maximal cliques in a thresholded correlation graph that can be easily constructed from the observed data. Our clique analysis technique scales well up to thousands of variables, while competing methods are not applicable in a reasonable amount of running time. We establish a finite-sample error bound and high-dimensional consistency for the structure learning of our method. Through a series of simulation studies and a real data example, we show that the CT algorithm is an accurate method for learning the structure of factor analysis models and is robust to violations of its assumptions.

In neural Information Retrieval, ongoing research is directed towards improving the first retriever in ranking pipelines. Learning dense embeddings to conduct retrieval using efficient approximate nearest neighbors methods has proven to work well. Meanwhile, there has been a growing interest in learning sparse representations for documents and queries, that could inherit from the desirable properties of bag-of-words models such as the exact matching of terms and the efficiency of inverted indexes. In this work, we present a new first-stage ranker based on explicit sparsity regularization and a log-saturation effect on term weights, leading to highly sparse representations and competitive results with respect to state-of-the-art dense and sparse methods. Our approach is simple, trained end-to-end in a single stage. We also explore the trade-off between effectiveness and efficiency, by controlling the contribution of the sparsity regularization.

Real-world large-scale datasets are both noisily labeled and class-imbalanced. The issues seriously hurt the generalization of trained models. It is hence significant to address the simultaneous incorrect labeling and class-imbalance, i.e., the problem of learning with noisy labels on long-tailed data. Previous works develop several methods for the problem. However, they always rely on strong assumptions that are invalid or hard to be checked in practice. In this paper, to handle the problem and address the limitations of prior works, we propose a representation calibration method RCAL. Specifically, RCAL works with the representations extracted by unsupervised contrastive learning. We assume that without incorrect labeling and class imbalance, the representations of instances in each class conform to a multivariate Gaussian distribution, which is much milder and easier to be checked. Based on the assumption, we recover underlying representation distributions from polluted ones resulting from mislabeled and class-imbalanced data. Additional data points are then sampled from the recovered distributions to help generalization. Moreover, during classifier training, representation learning takes advantage of representation robustness brought by contrastive learning, which further improves the classifier performance. We derive theoretical results to discuss the effectiveness of our representation calibration. Experiments on multiple benchmarks justify our claims and confirm the superiority of the proposed method.

Novel Class Discovery (NCD) is a growing field where we are given during training a labeled set of known classes and an unlabeled set of different classes that must be discovered. In recent years, many methods have been proposed to address this problem, and the field has begun to mature. In this paper, we provide a comprehensive survey of the state-of-the-art NCD methods. We start by formally defining the NCD problem and introducing important notions. We then give an overview of the different families of approaches, organized by the way they transfer knowledge from the labeled set to the unlabeled set. We find that they either learn in two stages, by first extracting knowledge from the labeled data only and then applying it to the unlabeled data, or in one stage by conjointly learning on both sets. For each family, we describe their general principle and detail a few representative methods. Then, we briefly introduce some new related tasks inspired by the increasing number of NCD works. We also present some common tools and techniques used in NCD, such as pseudo labeling, self-supervised learning and contrastive learning. Finally, to help readers unfamiliar with the NCD problem differentiate it from other closely related domains, we summarize some of the closest areas of research and discuss their main differences.

We introduce in this paper the mechanism of graph random features (GRFs). GRFs can be used to construct unbiased randomized estimators of several important kernels defined on graphs' nodes, in particular the regularized Laplacian kernel. As regular RFs for non-graph kernels, they provide means to scale up kernel methods defined on graphs to larger networks. Importantly, they give substantial computational gains also for smaller graphs, while applied in downstream applications. Consequently, GRFs address the notoriously difficult problem of cubic (in the number of the nodes of the graph) time complexity of graph kernels algorithms. We provide a detailed theoretical analysis of GRFs and an extensive empirical evaluation: from speed tests, through Frobenius relative error analysis to kmeans graph-clustering with graph kernels. We show that the computation of GRFs admits an embarrassingly simple distributed algorithm that can be applied if the graph under consideration needs to be split across several machines. We also introduce a (still unbiased) quasi Monte Carlo variant of GRFs, q-GRFs, relying on the so-called reinforced random walks, that might be used to optimize the variance of GRFs. As a byproduct, we obtain a novel approach to solve certain classes of linear equations with positive and symmetric matrices.

Deep metric learning has been widely applied in many computer vision tasks, and recently, it is more attractive in zero-shot image retrieval and clustering(ZSRC) where a good embedding is requested such that the unseen classes can be distinguished well. Most existing works deem this 'good' embedding just to be the discriminative one and thus race to devise powerful metric objectives or hard-sample mining strategies for leaning discriminative embedding. However, in this paper, we first emphasize that the generalization ability is a core ingredient of this 'good' embedding as well and largely affects the metric performance in zero-shot settings as a matter of fact. Then, we propose the Energy Confused Adversarial Metric Learning(ECAML) framework to explicitly optimize a robust metric. It is mainly achieved by introducing an interesting Energy Confusion regularization term, which daringly breaks away from the traditional metric learning idea of discriminative objective devising, and seeks to 'confuse' the learned model so as to encourage its generalization ability by reducing overfitting on the seen classes. We train this confusion term together with the conventional metric objective in an adversarial manner. Although it seems weird to 'confuse' the network, we show that our ECAML indeed serves as an efficient regularization technique for metric learning and is applicable to various conventional metric methods. This paper empirically and experimentally demonstrates the importance of learning embedding with good generalization, achieving state-of-the-art performances on the popular CUB, CARS, Stanford Online Products and In-Shop datasets for ZSRC tasks. \textcolor[rgb]{1, 0, 0}{Code available at http://www.bhchen.cn/}.

This paper studies the fair range clustering problem in which the data points are from different demographic groups and the goal is to pick k centers with the minimum clustering cost such that each group is at least minimally represented in the centers set and no group dominates the centers set. More precisely, given a set of n points in a metric space (P,d) where each point belongs to one of the ell different demographics (i.e., P = P_1 uplus P_2 uplus cdots uplus P_ell) and a set of ell intervals [alpha_1, beta_1], cdots, [alpha_ell, beta_ell] on desired number of centers from each group, the goal is to pick a set of k centers C with minimum ell_p-clustering cost (i.e., (sum_{vin P} d(v,C)^p)^{1/p}) such that for each group iin ell, |Ccap P_i| in [alpha_i, beta_i]. In particular, the fair range ell_p-clustering captures fair range k-center, k-median and k-means as its special cases. In this work, we provide efficient constant factor approximation algorithms for fair range ell_p-clustering for all values of pin [1,infty).

The kernel thinning (KT) algorithm of Dwivedi and Mackey (2021) compresses a probability distribution more effectively than independent sampling by targeting a reproducing kernel Hilbert space (RKHS) and leveraging a less smooth square-root kernel. Here we provide four improvements. First, we show that KT applied directly to the target RKHS yields tighter, dimension-free guarantees for any kernel, any distribution, and any fixed function in the RKHS. Second, we show that, for analytic kernels like Gaussian, inverse multiquadric, and sinc, target KT admits maximum mean discrepancy (MMD) guarantees comparable to or better than those of square-root KT without making explicit use of a square-root kernel. Third, we prove that KT with a fractional power kernel yields better-than-Monte-Carlo MMD guarantees for non-smooth kernels, like Laplace and Mat\'ern, that do not have square-roots. Fourth, we establish that KT applied to a sum of the target and power kernels (a procedure we call KT+) simultaneously inherits the improved MMD guarantees of power KT and the tighter individual function guarantees of target KT. In our experiments with target KT and KT+, we witness significant improvements in integration error even in 100 dimensions and when compressing challenging differential equation posteriors.

We study the estimation of a planted signal hidden in a recently introduced nested matrix-tensor model, which is an extension of the classical spiked rank-one tensor model, motivated by multi-view clustering. Prior work has theoretically examined the performance of a tensor-based approach, which relies on finding a best rank-one approximation, a problem known to be computationally hard. A tractable alternative approach consists in computing instead the best rank-one (matrix) approximation of an unfolding of the observed tensor data, but its performance was hitherto unknown. We quantify here the performance gap between these two approaches, in particular by deriving the precise algorithmic threshold of the unfolding approach and demonstrating that it exhibits a BBP-type transition behavior. This work is therefore in line with recent contributions which deepen our understanding of why tensor-based methods surpass matrix-based methods in handling structured tensor data.

We present a novel framework, i.e., Segment Any Anomaly + (SAA+), for zero-shot anomaly segmentation with hybrid prompt regularization to improve the adaptability of modern foundation models. Existing anomaly segmentation models typically rely on domain-specific fine-tuning, limiting their generalization across countless anomaly patterns. In this work, inspired by the great zero-shot generalization ability of foundation models like Segment Anything, we first explore their assembly to leverage diverse multi-modal prior knowledge for anomaly localization. For non-parameter foundation model adaptation to anomaly segmentation, we further introduce hybrid prompts derived from domain expert knowledge and target image context as regularization. Our proposed SAA+ model achieves state-of-the-art performance on several anomaly segmentation benchmarks, including VisA, MVTec-AD, MTD, and KSDD2, in the zero-shot setting. We will release the code at https://github.com/caoyunkang/Segment-Any-Anomaly{https://github.com/caoyunkang/Segment-Any-Anomaly}.

We present a detailed theoretical and computational analysis of the Watset meta-algorithm for fuzzy graph clustering, which has been found to be widely applicable in a variety of domains. This algorithm creates an intermediate representation of the input graph that reflects the "ambiguity" of its nodes. Then, it uses hard clustering to discover clusters in this "disambiguated" intermediate graph. After outlining the approach and analyzing its computational complexity, we demonstrate that Watset shows competitive results in three applications: unsupervised synset induction from a synonymy graph, unsupervised semantic frame induction from dependency triples, and unsupervised semantic class induction from a distributional thesaurus. Our algorithm is generic and can be also applied to other networks of linguistic data.

Block coordinate descent (BCD) methods are widely used for large-scale numerical optimization because of their cheap iteration costs, low memory requirements, amenability to parallelization, and ability to exploit problem structure. Three main algorithmic choices influence the performance of BCD methods: the block partitioning strategy, the block selection rule, and the block update rule. In this paper we explore all three of these building blocks and propose variations for each that can significantly improve the progress made by each BCD iteration. We (i) propose new greedy block-selection strategies that guarantee more progress per iteration than the Gauss-Southwell rule; (ii) explore practical issues like how to implement the new rules when using "variable" blocks; (iii) explore the use of message-passing to compute matrix or Newton updates efficiently on huge blocks for problems with sparse dependencies between variables; and (iv) consider optimal active manifold identification, which leads to bounds on the "active-set complexity" of BCD methods and leads to superlinear convergence for certain problems with sparse solutions (and in some cases finite termination at an optimal solution). We support all of our findings with numerical results for the classic machine learning problems of least squares, logistic regression, multi-class logistic regression, label propagation, and L1-regularization.

Faithful visualizations of data residing on manifolds must take the underlying geometry into account when producing a flat planar view of the data. In this paper, we extend the classic stochastic neighbor embedding (SNE) algorithm to data on general Riemannian manifolds. We replace standard Gaussian assumptions with Riemannian diffusion counterparts and propose an efficient approximation that only requires access to calculations of Riemannian distances and volumes. We demonstrate that the approach also allows for mapping data from one manifold to another, e.g. from a high-dimensional sphere to a low-dimensional one.

Machine learning models -- including prominent zero-shot models -- are often trained on datasets whose labels are only a small proportion of a larger label space. Such spaces are commonly equipped with a metric that relates the labels via distances between them. We propose a simple approach to exploit this information to adapt the trained model to reliably predict new classes -- or, in the case of zero-shot prediction, to improve its performance -- without any additional training. Our technique is a drop-in replacement of the standard prediction rule, swapping argmax with the Fr\'echet mean. We provide a comprehensive theoretical analysis for this approach, studying (i) learning-theoretic results trading off label space diameter, sample complexity, and model dimension, (ii) characterizations of the full range of scenarios in which it is possible to predict any unobserved class, and (iii) an optimal active learning-like next class selection procedure to obtain optimal training classes for when it is not possible to predict the entire range of unobserved classes. Empirically, using easily-available external metrics, our proposed approach, Loki, gains up to 29.7% relative improvement over SimCLR on ImageNet and scales to hundreds of thousands of classes. When no such metric is available, Loki can use self-derived metrics from class embeddings and obtains a 10.5% improvement on pretrained zero-shot models such as CLIP.

Mixture of experts (MoE) has a well-principled finite mixture model construction for prediction, allowing the gating network (mixture weights) to learn from the predictors (explanatory variables) together with the experts' network (mixture component densities). We investigate the estimation properties of MoEs in a high-dimensional setting, where the number of predictors is much larger than the sample size, for which the literature lacks computational and especially theoretical results. We consider the class of finite MoE models with softmax gating functions and Gaussian regression experts, and focus on the theoretical properties of their l_1-regularized estimation via the Lasso. We provide a lower bound on the regularization parameter of the Lasso penalty that ensures an l_1-oracle inequality is satisfied by the Lasso estimator according to the Kullback--Leibler loss. We further state an l_1-ball oracle inequality for the l_1-penalized maximum likelihood estimator from the model selection.

The acquisition of labels for supervised learning can be expensive. To improve the sample efficiency of neural network regression, we study active learning methods that adaptively select batches of unlabeled data for labeling. We present a framework for constructing such methods out of (network-dependent) base kernels, kernel transformations, and selection methods. Our framework encompasses many existing Bayesian methods based on Gaussian process approximations of neural networks as well as non-Bayesian methods. Additionally, we propose to replace the commonly used last-layer features with sketched finite-width neural tangent kernels and to combine them with a novel clustering method. To evaluate different methods, we introduce an open-source benchmark consisting of 15 large tabular regression data sets. Our proposed method outperforms the state-of-the-art on our benchmark, scales to large data sets, and works out-of-the-box without adjusting the network architecture or training code. We provide open-source code that includes efficient implementations of all kernels, kernel transformations, and selection methods, and can be used for reproducing our results.

It is impossible today to pretend that the practice of machine learning is compatible with the idea that training and testing data follow the same distribution. Several authors have recently used ensemble techniques to show how scenarios involving multiple data distributions are best served by representations that are both richer than those obtained by regularizing for the best in-distribution performance, and richer than those obtained under the influence of the implicit sparsity bias of common stochastic gradient procedures. This contribution investigates the use of very high dropout rates instead of ensembles to obtain such rich representations. Although training a deep network from scratch using such dropout rates is virtually impossible, fine-tuning a large pre-trained model under such conditions is not only possible but also achieves out-of-distribution performances that exceed those of both ensembles and weight averaging methods such as model soups. This result has practical significance because the importance of the fine-tuning scenario has considerably grown in recent years. This result also provides interesting insights on the nature of rich representations and on the intrinsically linear nature of fine-tuning a large network using a comparatively small dataset.

We address the problem of learning the dynamics of an unknown non-parametric system linking a target and a feature time series. The feature time series is measured on a sparse and irregular grid, while we have access to only a few points of the target time series. Once learned, we can use these dynamics to predict values of the target from the previous values of the feature time series. We frame this task as learning the solution map of a controlled differential equation (CDE). By leveraging the rich theory of signatures, we are able to cast this non-linear problem as a high-dimensional linear regression. We provide an oracle bound on the prediction error which exhibits explicit dependencies on the individual-specific sampling schemes. Our theoretical results are illustrated by simulations which show that our method outperforms existing algorithms for recovering the full time series while being computationally cheap. We conclude by demonstrating its potential on real-world epidemiological data.

k-Clustering in R^d (e.g., k-median and k-means) is a fundamental machine learning problem. While near-linear time approximation algorithms were known in the classical setting for a dataset with cardinality n, it remains open to find sublinear-time quantum algorithms. We give quantum algorithms that find coresets for k-clustering in R^d with O(nkd^{3/2}) query complexity. Our coreset reduces the input size from n to poly(kepsilon^{-1}d), so that existing alpha-approximation algorithms for clustering can run on top of it and yield (1 + epsilon)alpha-approximation. This eventually yields a quadratic speedup for various k-clustering approximation algorithms. We complement our algorithm with a nearly matching lower bound, that any quantum algorithm must make Omega(nk) queries in order to achieve even O(1)-approximation for k-clustering.

Representing a manifold of very high-dimensional data with generative models has been shown to be computationally efficient in practice. However, this requires that the data manifold admits a global parameterization. In order to represent manifolds of arbitrary topology, we propose to learn a mixture model of variational autoencoders. Here, every encoder-decoder pair represents one chart of a manifold. We propose a loss function for maximum likelihood estimation of the model weights and choose an architecture that provides us the analytical expression of the charts and of their inverses. Once the manifold is learned, we use it for solving inverse problems by minimizing a data fidelity term restricted to the learned manifold. To solve the arising minimization problem we propose a Riemannian gradient descent algorithm on the learned manifold. We demonstrate the performance of our method for low-dimensional toy examples as well as for deblurring and electrical impedance tomography on certain image manifolds.

We present CLUSTSEG, a general, transformer-based framework that tackles different image segmentation tasks (i.e., superpixel, semantic, instance, and panoptic) through a unified neural clustering scheme. Regarding queries as cluster centers, CLUSTSEG is innovative in two aspects:1) cluster centers are initialized in heterogeneous ways so as to pointedly address task-specific demands (e.g., instance- or category-level distinctiveness), yet without modifying the architecture; and 2) pixel-cluster assignment, formalized in a cross-attention fashion, is alternated with cluster center update, yet without learning additional parameters. These innovations closely link CLUSTSEG to EM clustering and make it a transparent and powerful framework that yields superior results across the above segmentation tasks.

Two different approaches exist to handle missing values for prediction: either imputation, prior to fitting any predictive algorithms, or dedicated methods able to natively incorporate missing values. While imputation is widely (and easily) use, it is unfortunately biased when low-capacity predictors (such as linear models) are applied afterward. However, in practice, naive imputation exhibits good predictive performance. In this paper, we study the impact of imputation in a high-dimensional linear model with MCAR missing data. We prove that zero imputation performs an implicit regularization closely related to the ridge method, often used in high-dimensional problems. Leveraging on this connection, we establish that the imputation bias is controlled by a ridge bias, which vanishes in high dimension. As a predictor, we argue in favor of the averaged SGD strategy, applied to zero-imputed data. We establish an upper bound on its generalization error, highlighting that imputation is benign in the d sqrt n regime. Experiments illustrate our findings.

Regularization is a set of techniques that are used to improve the generalization ability of deep neural networks. In this paper, we introduce weight compander (WC), a novel effective method to improve generalization by reparameterizing each weight in deep neural networks using a nonlinear function. It is a general, intuitive, cheap and easy to implement method, which can be combined with various other regularization techniques. Large weights in deep neural networks are a sign of a more complex network that is overfitted to the training data. Moreover, regularized networks tend to have a greater range of weights around zero with fewer weights centered at zero. We introduce a weight reparameterization function which is applied to each weight and implicitly reduces overfitting by restricting the magnitude of the weights while forcing them away from zero at the same time. This leads to a more democratic decision-making in the network. Firstly, individual weights cannot have too much influence in the prediction process due to the restriction of their magnitude. Secondly, more weights are used in the prediction process, since they are forced away from zero during the training. This promotes the extraction of more features from the input data and increases the level of weight redundancy, which makes the network less sensitive to statistical differences between training and test data. We extend our method to learn the hyperparameters of the introduced weight reparameterization function. This avoids hyperparameter search and gives the network the opportunity to align the weight reparameterization with the training progress. We show experimentally that using weight compander in addition to standard regularization methods improves the performance of neural networks.

Electronic Health Records (EHR) are high-dimensional data with implicit connections among thousands of medical concepts. These connections, for instance, the co-occurrence of diseases and lab-disease correlations can be informative when only a subset of these variables is documented by the clinician. A feasible approach to improving the representation learning of EHR data is to associate relevant medical concepts and utilize these connections. Existing medical ontologies can be the reference for EHR structures, but they place numerous constraints on the data source. Recent progress on graph neural networks (GNN) enables end-to-end learning of topological structures for non-grid or non-sequential data. However, there are problems to be addressed on how to learn the medical graph adaptively and how to understand the effect of the medical graph on representation learning. In this paper, we propose a variationally regularized encoder-decoder graph network that achieves more robustness in graph structure learning by regularizing node representations. Our model outperforms the existing graph and non-graph based methods in various EHR predictive tasks based on both public data and real-world clinical data. Besides the improvements in empirical experiment performances, we provide an interpretation of the effect of variational regularization compared to standard graph neural network, using singular value analysis.

We rigorously quantify the improvement in the sample complexity of variational divergence estimations for group-invariant distributions. In the cases of the Wasserstein-1 metric and the Lipschitz-regularized alpha-divergences, the reduction of sample complexity is proportional to an ambient-dimension-dependent power of the group size. For the maximum mean discrepancy (MMD), the improvement of sample complexity is more nuanced, as it depends on not only the group size but also the choice of kernel. Numerical simulations verify our theories.

Existing graph matching methods typically assume that there are similar structures between graphs and they are matchable. However, these assumptions do not align with real-world applications. This work addresses a more realistic scenario where graphs exhibit diverse modes, requiring graph grouping before or along with matching, a task termed mixture graph matching and clustering. We introduce Minorize-Maximization Matching and Clustering (M3C), a learning-free algorithm that guarantees theoretical convergence through the Minorize-Maximization framework and offers enhanced flexibility via relaxed clustering. Building on M3C, we develop UM3C, an unsupervised model that incorporates novel edge-wise affinity learning and pseudo label selection. Extensive experimental results on public benchmarks demonstrate that our method outperforms state-of-the-art graph matching and mixture graph matching and clustering approaches in both accuracy and efficiency. Source code will be made publicly available.

Unsupervised representation learning with contrastive learning achieved great success. This line of methods duplicate each training batch to construct contrastive pairs, making each training batch and its augmented version forwarded simultaneously and leading to additional computation. We propose a new jigsaw clustering pretext task in this paper, which only needs to forward each training batch itself, and reduces the training cost. Our method makes use of information from both intra- and inter-images, and outperforms previous single-batch based ones by a large margin. It is even comparable to the contrastive learning methods when only half of training batches are used. Our method indicates that multiple batches during training are not necessary, and opens the door for future research of single-batch unsupervised methods. Our models trained on ImageNet datasets achieve state-of-the-art results with linear classification, outperforming previous single-batch methods by 2.6%. Models transferred to COCO datasets outperform MoCo v2 by 0.4% with only half of the training batches. Our pretrained models outperform supervised ImageNet pretrained models on CIFAR-10 and CIFAR-100 datasets by 0.9% and 4.1% respectively. Code is available at https://github.com/Jia-Research-Lab/JigsawClustering

Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step followed by a projection-based measurement consistency step, often produce suboptimal results. By studying the generative sampling path, here we show that current solvers throw the sample path off the data manifold, and hence the error accumulates. To address this, we propose an additional correction term inspired by the manifold constraint, which can be used synergistically with the previous solvers to make the iterations close to the manifold. The proposed manifold constraint is straightforward to implement within a few lines of code, yet boosts the performance by a surprisingly large margin. With extensive experiments, we show that our method is superior to the previous methods both theoretically and empirically, producing promising results in many applications such as image inpainting, colorization, and sparse-view computed tomography. Code available https://github.com/HJ-harry/MCG_diffusion

We propose UnMixMatch, a semi-supervised learning framework which can learn effective representations from unconstrained unlabelled data in order to scale up performance. Most existing semi-supervised methods rely on the assumption that labelled and unlabelled samples are drawn from the same distribution, which limits the potential for improvement through the use of free-living unlabeled data. Consequently, the generalizability and scalability of semi-supervised learning are often hindered by this assumption. Our method aims to overcome these constraints and effectively utilize unconstrained unlabelled data in semi-supervised learning. UnMixMatch consists of three main components: a supervised learner with hard augmentations that provides strong regularization, a contrastive consistency regularizer to learn underlying representations from the unlabelled data, and a self-supervised loss to enhance the representations that are learnt from the unlabelled data. We perform extensive experiments on 4 commonly used datasets and demonstrate superior performance over existing semi-supervised methods with a performance boost of 4.79%. Extensive ablation and sensitivity studies show the effectiveness and impact of each of the proposed components of our method.

Contrastive learning is a powerful self-supervised learning method, but we have a limited theoretical understanding of how it works and why it works. In this paper, we prove that contrastive learning with the standard InfoNCE loss is equivalent to spectral clustering on the similarity graph. Using this equivalence as the building block, we extend our analysis to the CLIP model and rigorously characterize how similar multi-modal objects are embedded together. Motivated by our theoretical insights, we introduce the kernel mixture loss, incorporating novel kernel functions that outperform the standard Gaussian kernel on several vision datasets.

We introduce a Parametric Information Maximization (PIM) model for the Generalized Category Discovery (GCD) problem. Specifically, we propose a bi-level optimization formulation, which explores a parameterized family of objective functions, each evaluating a weighted mutual information between the features and the latent labels, subject to supervision constraints from the labeled samples. Our formulation mitigates the class-balance bias encoded in standard information maximization approaches, thereby handling effectively both short-tailed and long-tailed data sets. We report extensive experiments and comparisons demonstrating that our PIM model consistently sets new state-of-the-art performances in GCD across six different datasets, more so when dealing with challenging fine-grained problems.

In this paper we introduce Feature Gradients, a gradient-based search algorithm for feature selection. Our approach extends a recent result on the estimation of learnability in the sublinear data regime by showing that the calculation can be performed iteratively (i.e., in mini-batches) and in linear time and space with respect to both the number of features D and the sample size N . This, along with a discrete-to-continuous relaxation of the search domain, allows for an efficient, gradient-based search algorithm among feature subsets for very large datasets. Crucially, our algorithm is capable of finding higher-order correlations between features and targets for both the N > D and N < D regimes, as opposed to approaches that do not consider such interactions and/or only consider one regime. We provide experimental demonstration of the algorithm in small and large sample-and feature-size settings.

Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible in closed form, so prior methods resort to imprecise approximations of the score matching training objective that degrade performance and preclude applications in high dimensions. In this work, we reexamine these approximations and propose several practical improvements. Our key observation is that most relevant manifolds are symmetric spaces, which are much more amenable to computation. By leveraging and combining various ans\"{a}tze, we can quickly compute relevant quantities to high precision. On low dimensional datasets, our correction produces a noticeable improvement, allowing diffusion to compete with other methods. Additionally, we show that our method enables us to scale to high dimensional tasks on nontrivial manifolds. In particular, we model QCD densities on SU(n) lattices and contrastively learned embeddings on high dimensional hyperspheres.

While Self-Supervised Learning has helped reap the benefit of the scale from the available unlabeled data, the learning paradigms are continuously being bettered. We present a new pre-training strategy named ccc-wav2vec 2.0, which uses clustering and an augmentation-based cross-contrastive loss as its self-supervised objective. Through the clustering module, we scale down the influence of those negative examples that are highly similar to the positive. The Cross-Contrastive loss is computed between the encoder output of the original sample and the quantizer output of its augmentation and vice-versa, bringing robustness to the pre-training strategy. ccc-wav2vec 2.0 achieves up to 15.6% and 12.7% relative WER improvement over the baseline wav2vec 2.0 on the test-clean and test-other sets, respectively, of LibriSpeech, without the use of any language model. The proposed method also achieves up to 14.9% relative WER improvement over the baseline wav2vec 2.0 when fine-tuned on Switchboard data. We make all our codes publicly available on GitHub.