Unsupervised Clustering

Turning movement counts are essential for intersection-level traffic management, yet their collection remains predominantly manual due to the cost of per-camera region annotation. This paper presents an unsupervised pipeline that identifies entry and exit regions directly from raw vehicle trajectories extracted via object detection and multi-object tracking, requiring no manual annotation, camera calibration, or prior knowledge of intersection geometry. Unlike trajectory clustering methods that classify individual trajectories using pairwise similarity and must be re-executed on every new batch, the proposed pipeline clusters initial and terminal point locations to produce persistent spatial region polygons that classify future trajectories by point-in-polygon containment at linear cost. The pipeline comprises six sequential steps, five of which introduce configurable parameters evaluated through a systematic statistical analysis spanning 17,100 pipeline executions across 9 surveillance cameras capturing dense heterogeneous traffic in Bengaluru, India, and 10 sequences from the UA-DETRAC benchmark dataset. Both parametric and nonparametric testing frameworks identify three consistently significant parameters and yield an empirically grounded recommended configuration. Under this configuration, the pipeline achieves a median classification error of 3.4% across all 25 Bengaluru cameras, including 16 held-out locations, with a median per-turning-movement GEH of 2.43. Compared with two trajectory clustering baselines, the proposed pipeline exhibits greater stability across camera views and lower computational cost, at the expense of higher median error. Extended evaluation demonstrates that calibration clips of at least 60 minutes and peak-traffic selection further improve region estimation quality.

Pseudo-labeling based on Optimal Transport (OT) has become an effective mechanism for enhancing short text clustering. Existing OT methods are short in modeling semantic consistencies between samples, which may assign different pseudo-labels to semantically similar samples. These erroneous pseudo-labels can cause the model to produce inferior clusters. This paper proposes a novel short text clustering framework, which remedies the neglect of semantic consistency in existing OT methods, generating reliable pseudo-labels to facilitate clustering. Specifically, the proposed approach first designs an instance-level attention mechanism to capture semantic relationships between samples, which are then integrated into the OT formulation to endow the transport process with neighborhood semantic awareness. By solving the proposed OT formulation, reliable pseudo-labels are obtained that simultaneously account for sample-to-sample semantic consistency and sample-to-cluster global structure information. These pseudo-labels are then used as supervisory signals to guide the model to achieve accurate clustering. Extensive experiments demonstrate that the proposed approach outperforms state-of-the-art methods. The code is available at: https://github.com/YZH0905/CAOT-STC.

In many realistic scenarios, large volumes of time series data are generated with limited or expensive annotations. This limitation makes supervised learning methods difficult to apply and leads to the use of unsupervised approaches capable of discovering meaningful structures directly from raw data. Clustering therefore plays a crucial role in organizing time series into groups that share similar temporal patterns, enabling exploratory analysis and downstream tasks without requiring manual labeling. However, existing deep clustering methods often struggle to capture long-range temporal dependencies or rely on architectures with high computational cost. This paper introduces FMMVCC, a Mamba-based deep clustering framework for time series that leverages state space sequence modeling to efficiently learn temporal representations with linear complexity. Additionally, it utilizes multi-view self-supervised learning with temporal masking and augmentations. Experimental evaluation in 15 benchmark datasets proves that FMMVCC consistently outperforms state-of-the-art baselines, achieving the best overall performance in 29 of 60 total metric evaluations and the highest average rank in all tested scenarios.

Missing data is prevalent in practical applications, making effective imputation an essential preprocessing step for downstream analysis. Real-world datasets often exhibit complex latent structures composed of multiple subgroups with distinct distributions. However, existing methods often overlook such population heterogeneity. Without explicit structural guidance, these methods tend to produce generic estimates that blur subgroup boundaries and lack instance-level fidelity. While incorporating subgroup information offers a remedy, it faces a circular dependency: reliable subgroup identification requires complete data, while data completion is the imputation objective itself. To resolve this, we propose CAGI (Cluster-Aware Generative Imputation), a framework that reformulates clustering and imputation as a mutually reinforcing co-optimization process. CAGI employs a ``Partition-Guide-Restore'' strategy where dynamic cluster assignments act as local priors to condition a Generative Adversarial Network. An iterative feedback loop is established to progressively refine both cluster structures and imputed values toward faithful subgroup distributions. To ensure distributional stability, CAGI further employs a multi-level optimization objective combining instance-level reconstruction with distribution-level regularization. Extensive experiments on 14 benchmark datasets with 15 representative baselines demonstrate the superiority of CAGI. The source code is available at: https://github.com/supercocachii/CAGI

A variety of self-supervised image clustering approaches are invented in the past years. However, all dominant approaches are exploitative: The direction of parameter updates is determined by known states (observed input samples and existing parameters). We propose an explorative self-supervised learning framework that steps out of this zone. We define a surprise score that measures how unlikely the model's output representation is, assuming that all pixels are i.i.d. random noise. Maximizing the surprise score forces the deep learning model to reject the random noise null hypothesis, or equivalently, to discover non-randomness from data. Also, we propose a fundamental assumption: a surprise score cannot, in general, be fully optimized by exploitative optimization approaches. Thus, we propose the converge-to-surprise scheme to optimize a model: an evolution-strategy (ES) outer loop, which maximizes the surprise score using the mutation-selection mechanism, paired with a periodic gradient-descent inner loop, which uses the surprising clusters already discovered by ES as surrogate targets. On simple image benchmarks, our framework trained from scratch achieves new state-of-the-art results in non-parametric self-supervised image clustering --- the strictest deep-clustering setting, where the number of classes is unknown during training.

Incomplete Multi-View Clustering addresses the problem of clustering multi-modal data when certain views are missing. Recent end-to-end generative approaches leverage diffusion models to recover missing views via stochastic noise-to-data trajectories. While expressive, such mechanisms are not explicitly designed for clustering, as they initialize from cluster-agnostic noise and rely on stochastic denoising dynamics. In this work, we revisit probability path design in end-to-end generative IMVC. We introduce a flow-matching framework with a linear interpolation path between paired view representations, that replaces diffusion with probability flows between observed and missing views. We provide a formal analysis showing that deterministic ODE flows are inherently better aligned with clustering objectives than diffusion-based stochastic trajectories, especially in terms of transport mechanisms that respect class-conditional data distributions and maintain cluster consistency in finite-step regimes. Building upon this insight, we develop an end-to-end IMVC architecture that integrates straight-path flow-matching view completion with cluster-level and entropy-based alignment to enforce cross-view clustering consistency. Extensive experiments on standard IMVC benchmarks demonstrate that the proposed framework establishes new state-of-the-art performance.

The classical $k$-means clustering cannot be directly used to incomplete data, and existing $k$-means-based clustering for missing data primarily focus on improving the practical accuracy of clustering, whereas most of them lack theoretical guarantees in the asymptotic sense. In this paper, we investigate the statistical properties of $k$-means clustering in the presence of missing data. We first establish the $\sqrt{n}$-excess risk bound and prove the consistency of the estimated cluster centers under general missing mechanisms. For the Missing Completely at Random (MCAR) mechanism, we further derive the $\sqrt{n}$-convergence rate and asymptotic normality of the estimated cluster centers. Moreover, we study in what cases the cluster centers estimated by incomplete data converge to the true cluster centers of original fully observed data, and give a sufficient condition about the missing probability and the separation among true clusters. These results provide a theoretical guarantee for missing-data-$k$-means. Notably, our analysis reveal that under MCAR mechanism, both achieving the $\sqrt{n}$-rate and converging to the true cluster centers require $k$ true centers to be distinct in every dimension, highlighting the significant challenges of application in high-dimensional regimes. Finally, we conduct numerical simulations on synthetic incomplete datasets to support our theoretical analysis results.

The classical $k$-means clustering, based on distances computed from all data features, cannot be directly applied to incomplete data with missing values. A natural extension of $k$-means to missing data is to involve only the observed positions in clustering, which is equivalent to imputing missing values by corresponding cluster means. However, for data missing not at random (MNAR), since missingness is related to data values, such a mean-imputation-based method may lead to the distortion of estimated cluster centers, resulting in a poor clustering result. Since MNAR mechanisms are very common in reality, it is necessary to improve the performance of $k$-means-based clustering methods for such data. In this paper, we focus on a magnitude-decaying MNAR scenario where data is more likely to be missing at positions with smaller absolute values, and we propose a novel $k$-means clustering method based on the constraint of the size of imputation values, which enjoys a good mathematical interpretation. Moreover, we establish the statistical consistency of the estimated cluster centers of the proposed method to the true cluster centers of fully observed data, and solve the optimization of the proposed loss function via an alternative minimization algorithm. Simulation experiments verify the effect of the proposed method in improving clustering results and reducing the bias of estimated cluster centers. Applications to real-world missing data further show the utility of the proposed method.

Federated Learning often suffers under non-independently and identically distributed data, where a single global model may fail to represent the diversity of client distributions. Clustered Federated Learning mitigates this issue by training specialized models for groups of similar clients, but existing approaches often couple cluster assignment with the main training loop, increasing computational and communication costs. We propose a lightweight clustering approach based on Random Network Distillation. Each client trains a compact Random Network Distillation predictor on its local data and uses its prediction error as a novelty signal to estimate similarity with other clients. This enables the discovery of meaningful client groups before federated training, without sharing raw data or repeatedly evaluating the main model. Crucially, the resulting federations emerge from local novelty estimates at runtime, making the method suitable for autonomous large-scale distributed systems where neither the number of clusters nor the collaboration structure can be specified a priori. Overall, by decoupling clustering from learning, the method provides a task-agnostic and efficient mechanism for autonomous collaboration under non-independently and identically distributed data.

Free-viewing gaze data provides a rich, task-free window into human visual attention. Conventional exploratory data analysis of the data provides user attention patterns through fixations and areas of interest. However, despite the richness of this gaze data, its human-information interaction (HII) patterns are understudied. We address this gap using consensus clustering of gaze data with respect to users and stimulus characteristics. We present a novel end-to-end unsupervised ensemble learning system for consensus clustering of free-viewing gaze datasets, EnsembleGaze. With a goal of characterizing the user behavior and stimulus type, we propose a feature engineering step based on statistical descriptors of fixation-based distributions. EnsembleGaze involves consensus voting of selected clustering methods implemented on the feature vector to compute the co-association matrix. Using the separate consensus clustering of users and stimuli as a baseline, we further propose two high-dimensional clustering strategies for determining gaze clusters based on joint user and image characterization. They are consensus subspace clustering and spectral biclustering. Clustering performance is evaluated using selected standard metrics and is further interpreted through image-level properties. Our system provides a replicable method for the unsupervised analysis of fixation behavior in scene perception research. Our results show that image stimuli groupings are highly consistent across methods, reflecting a robust ambient-versus-focal viewing mode distinction, whereas user groupings are image-context-dependent, a structure that only biclustering and the two-step conditional approaches are architecturally capable of recovering. Testing on the publicly available datasets revealed dataset-specific patterns, with each offering complementary insights through distinct clustering strategies.

Unifying image clustering across different clustering scenarios remains challenging due to fundamental gaps among tasks. We introduce a Guideline-Driven Image Clustering Agent, the first universal framework that bridges these gaps through textual guidelines. To incorporate complex guidelines without task-specific training, we propose Generative Concept Proxy Modeling, which generates guideline-aware embeddings via concept proxy extraction. For scenarios requiring automatic cluster discovery, we introduce LLM Traversal based on Minimum Spanning Tree that selectively applies LLM reasoning for complex semantic judgments. Our method generalizes across diverse clustering scenarios spanning from general to fine-grained categorization, from global to local criteria, and from balanced to long-tail distributions. Our framework consistently outperforms specialized methods across diverse clustering tasks.

In this article we describe Cohort Organized Learning (CoOL), a method for clustering data without explicit distance or similarity computations. Herein, we will describe CoOL, derive the gradients determined by expectation maximization to train the networks, show how to monitor convergence during training and evaluate the clusters after training, and discuss a series of examples and use cases. We also discuss CoOL's limitations and future prospects on related tasks. Because CoOL uses neural networks to estimate the clusters, it can be used to cluster any data that can be made compatible and we illustrate this on vector data and images.

We study the problem of system identification in heterogeneous settings, where different systems may follow distinct underlying dynamics. Existing clustered system identification approaches often rely on iterative training-based cluster assignment, which can be sensitive to learning uncertainty and model initialization. In contrast, we propose a one-shot, training-free clustering method that identifies similar systems using the structure of their locally observed data. Specifically, each system estimates a local state covariance matrix, and cluster identities are inferred by measuring the alignment between the leading covariance eigenspaces of different systems. We provide a mathematical interpretation of the proposed similarity score and develop a finite-sample analysis that characterizes how covariance estimation error induces eigenspace perturbations in terms of the underlying system dynamics. We then bound the probability of pairwise false eigenspace alignment and establish sufficient conditions for uniform inter-cluster eigenspace separation with high probability. Numerical experiments demonstrate that the proposed eigenspace-based clustering method effectively identifies systems with shared dynamics, leading to lower personalized model-estimation error compared with training-based clustering and non-clustered baselines.

Long-term human path forecasting in crowds is critical for autonomous moving platforms (like autonomous driving cars and social robots) to avoid collision and make high-quality planning. Although the current research take into account social interactions for prediction, they don't reveal the exact kinds of social interactions happened among people and how the social interactions affect the decision-making process of pedestrians, which further limits its robustness. Social interactions in pedestrian walking are intuitively massive and hard to label and quantify. In this paper, we explore creatively to quantify and interpret how pedestrians interact with others by proposing Learn to Cluster. Our clustering social interactions is probabilistic latent variable generative, learning directly from sequential trajectory observations, scalable to arbitrary number of pedestrians. Learn to cluster is label-free and can be naturally integrated into the training process of the prediction model. The latent variables will then serve as 'labels' to categorize social interactions. Extensive experiments over several trajectory prediction benchmarks demonstrate that our method is able to learn the patterns of social interactions and effectively integrate the patterns to pedestrian trajectory prediction.

This paper proposes an unsupervised workflow to pseudo-label extracellular spikes from human brain slice MEA recordings into two putative cell types: pyramidal cells and interneurons. Here, the raw data from the data acquisition system is used and processed. The pipeline for pre-processing includes bandpass filtering, threshold--based spike detection, frame alignment and normalization. In the ML workflow, dimensionality reduction (PCA, t-SNE, UMAP), clustering (GMM, k-means). To achieve an online system, template matching and OSort under varying curation strictness is also considered. All pipelines are evaluated by different cluster quality with within-cluster Pearson correlation, Silhouette score, and Calinski-Harabasz index. Applying stricter curation improves separation at some cost to inclusivity.

We propose a robust feature-weighted jump model for time-dependent clustering. A penalty is used to encourage smoothness of transitions over time, while robustness is achieved through the use of a Tukey's biweight loss function. An additional parameter controls the variability of feature weights across states, allowing the model to assign state-specific relevance to each feature. We illustrate in simulation how the method accurately recovers the true cluster sequence and reliably identifies relevant features, outperforming competing approaches, particularly in the presence of outliers. We conclude with two empirical applications, one on the number of conflict-related homicides in Kosovo in the period 1998-2000, and another on macroeconomic performance of twelve European countries in the period 1949-2024.

Clustering is fundamental to scRNA-seq analysis, serving as a cornerstone for identifying cell populations and resolving tissue heterogeneity. However, existing methods focus on mining numerical statistical patterns, suffering from semantic agnosticism by neglecting the intrinsic biological functions encoded by genes. While Large Language Models (LLMs) offer promising semantic capabilities, their direct adaptation to cell clustering is hindered by the structural mismatch between generative pre-training objectives and discriminative downstream tasks. To bridge this gap, we propose scLLM-DSC, a novel LLM-Knowledge Enhanced Cross-Modal Deep Structural Clustering framework. Diverging from data-driven paradigms, scLLM-DSC establishes a semantically-grounded representation by synergizing two views: a Knowledge-Driven Semantic View derived from NCBI gene priors and contextualized Cell2Sentence embeddings, and a Structure-Aware Topological View extracted via a graph-guided encoder. Crucially, we introduce a cross-modal contrastive alignment mechanism to enforce consistency between biological semantics and transcriptomic features within a unified latent space. Extensive benchmarks demonstrate that scLLM-DSC significantly outperforms eleven state-of-the-art baselines in clustering accuracy.

Unsupervised Continual Learning (UCL) aims to enable neural networks to learn sequential tasks without labels or access to past data. A major challenge in this setting is Catastrophic Forgetting, where models forget previously learned tasks upon learning new ones. This challenge is amplified in UCL due to the absence of labels to guide learning and memory retention. Existing mitigation strategies, such as knowledge distillation and replay buffers, often raise memory and privacy concerns. Moreover, current UCL methods largely overlook clustering-specific objectives. To fill this gap, we introduce Unsupervised Continual Clustering (UCC) and propose Forward-Backward Knowledge Distillation for Continual Clustering (FBCC). FBCC employs a continual teacher network with a clustering projector and lightweight task-specific students. Through a dual-phase forward-backward distillation process, the teacher learns new clusters while preserving previously discovered cluster structure without storing past data. FBCC represents a pioneering approach to UCC, demonstrating improved clustering performance across sequential tasks. Experiments on four benchmark datasets demonstrate that FBCC consistently outperforms existing continual learning baselines in clustering accuracy while significantly reducing catastrophic forgetting.

Huntington's disease (HD) is a progressive neurodegenerative disorder that affects motor, cognitive, and behavioral functions, where accurate characterization of disease progression remains essential to improve patient outcome and quality of life. Unsupervised machine learning (ML) approaches have demonstrated the ability to uncover disease progression trajectories and meaningful latent stages from longitudinal data; however, their limited interpretability restricts clinical trust and translation. We extend a previously proposed ML-based disease staging framework by applying an explainability analysis to the extracted feature representations and discovered disease stages. Applied to the Enroll-HD dataset, we first project the learned representations into a lower-dimensional space to intuitively assess whether the resulting clusters align with the progression of established clinical measures. We then use saliency maps to identify the clinical features that most strongly contribute to the learned embeddings over time. Finally, we train a surrogate classifier and apply SHAP to quantify feature importance for cluster assignments and to analyze which clinical variables drive transitions between disease stages. The explainability analysis indicates that the learned embeddings capture clinically meaningful disease structure, aligning with established motor and functional severity scores and exhibiting progressive deterioration across clusters. Within this analysis, SHAP reveals a stratification of disease stages, ranging from early cognitive-motor impairment to severe functional dependency, consistent with known clinical progression patterns, while also highlighting intra-stage variability.

Veterinary pharmacovigilance systems are essential for monitoring adverse drug events (ADEs), yet existing approaches often fail to capture region-specific toxicity patterns shaped by local biological and regulatory contexts. In Japan, these challenges are amplified by species-specific metabolic differences and reporting practices defined by the Ministry of Agriculture, Forestry, and Fisheries (MAFF). Most prior work relies on prediction-oriented models, limiting mechanistic interpretability. This study proposes a regulatory-integrated unsupervised framework for pattern discovery using the National Veterinary Assay Laboratory (NVAL) database. ADEs are encoded into organ system-aligned representations and adjusted for species-specific reporting biases, enabling cross-species comparison. Similarity-based clustering and dimensionality reduction are applied to identify latent toxicity structures. Analysis of 4,120 high-confidence ADE reports (9,080 drug-ADE combinations) identified three significant species clusters (p < 0.01), including hepatic-dominant patterns in companion animals (0.42 $\pm$ 0.06), renal toxicity in ruminants (0.39 $\pm$ 0.07), and dermatological sensitivity in sheep (0.35 $\pm$ 0.07). Drug-level clustering achieved 83% alignment with pharmacological classes, while cosine similarity outperformed alternative metrics (silhouette score: 0.48; cluster precision: 87%). Regulatory validation showed strong agreement with established classifications. These findings demonstrate that regulation-aligned unsupervised analysis can uncover biologically meaningful, region-specific toxicity patterns, providing an interpretable and scalable framework for veterinary drug safety assessment.

Huntington's disease (HD) is a progressive brain disorder that gradually affects movement, cognitive function, and behavior. Identifying the stage of the disease accurately and consistently is important for understanding its course, grouping patients, personalized care, and discovering treatment. Existing clinical staging frameworks rely primarily on predefined clinical measurement thresholds and clinical expert decisions, yet these discrete cut-offs may obscure meaningful intra-stage variability and remain vulnerable to inter-rater differences, especially in motor and functional assessments. To address these limitations, we developed an unsupervised machine learning framework based on dynamic graph representation learning to capture temporal relationships within and across patients from longitudinal clinical measurements. Using the learned representations, we applied K-means++ clustering to identify well-separated groups. We then iteratively increased the number of clusters (k), using stability analysis to assess robustness and reveal additional meaningful clusters beyond the initial optimal solution. We applied the framework to 302 individuals from the Enroll-HD cohort (1,477 visits, 44 clinical variables per visit; 80% manifest participants), enabling data-driven discovery of HD stages reflecting natural clinical progression. Despite the limited cohort size, the proposed framework achieved robust clustering performance using a four-dimensional latent space, identifying four meaningful and statistically distinct disease stages through clustering stability analysis. Each stage corresponded to well-defined clinical measurement boundaries, with minimal overlap compared to previously established clinical staging methods.

Building a lexicon from discovered word-like units is a central goal in zero-resource speech processing. But do our evaluations provide a trustworthy indication of lexicon quality? A common metric, normalized edit distance, averages the phoneme edit distances between discovered units in each cluster. We show that this metric has an inherent bias toward the quality of large clusters, inhibiting fair evaluation. Moreover, it ignores how well true classes are distributed across clusters. Based on established theory in clustering literature, we propose two metrics that address these shortcomings: a modified metric that weighs cluster size when assessing within-cluster consistency, and an inverse metric that assesses how true words are spread across clusters. Through experiments on synthetic and real-world lexicons, we demonstrate that combined, these metrics are: (1) more closely correlated with how similar a lexicon is to the ground-truth distribution, and (2) more robust to biases that skew lexicon evaluations.

Understanding activities of Internet scanners is challenging; it often requires identifying relationships between sources, a task for which semantic annotations are scarce. This work investigates whether semantically meaningful pairwise relationships between sequences of network flow records can be estimated by contrastive learning, without pretraining and without annotations. To this end, we propose a transformer model that embeds minimally preprocessed sequences of network flow records and train it using contrastive learning. With the similarities obtained from this model, we state a correlation clustering problem and solve it locally. Experimentally, we show: Learned similarities are higher on average for sequences originating from the same source than for sequences originating from different sources, and this property generalizes to unseen sequences of unseen sources. Moreover, correlation clustering yields clusters consistent with scanner labels. The complete source code of the algorithms and for reproducing the experiments is publicly available.

Real-world multi-view data always suffer from imperfect information problem, where the view-specific observations are absent (i.e., Incomplete Views, IV) and cross-view correspondences are mismatched (i.e., Noisy Correspondences, NC) for certain instances. As a remedy, numerous IV- and NC-oriented multi-view clustering (MvC) methods have been proposed, which however require either reliable correspondences or sufficiently complete instances, thus stopping short of addressing the imperfect information problem. In contrast, we observe that both IV and NC challenges originate from the same issue of imperfect cross-view counterpart information, where the counterpart of an anchor instance in another view might be either unavailable or unreliable. Based on the observation, we propose a novel robust MvC framework, termed Posterior-guided Latent Counterpart Inference (PLCI), which could handle both IV and NC in a unified manner. Specifically, PLCI formulates the desired cross-view counterpart of each anchor instance as a latent variable, and integrates both instance-level reliability and prototype-level semantic transport to infer the posterior distribution of the latent counterpart. Extensive experiments on six widely-used multi-view datasets against 10 state-of-the-art MvC methods demonstrate the effectiveness of PLCI for tackling the imperfect information problem. The code will be released upon acceptance.

Selecting a clustering algorithm and its hyperparameters without labels is a common difficulty in engineering machine learning pipelines that work with unsupervised analysis of sensor, image, or process data. Clustering validation indices (CVIs) provide internal scores for ranking candidate clusterings, but most popular CVIs are built from Euclidean compactness and separation terms and so tend to favour compact, convex partitions. Their performance is known to degrade on non convex, irregular, or variable density data, where kernel transformations or alternative distance measures are typically used at the cost of additional tuning and computation. This paper introduces the Central Description Length (CDL) clustering validation index. CDL uses the observed within cluster compactness, the estimated cluster centers, and the estimated cluster covariances to compute a probabilistic upper bound on the description length associated with the unobservable true cluster centers. The bound condenses intra cluster compactness and centroid displacement into a single computable quantity and is evaluated on the partition produced by any clustering algorithm. The implementation uses only observable quantities (the data, the partition, the estimated centers, and the estimated covariances) and does not use ground truth labels. On synthetic benchmarks with non convex and arbitrary shape clusters, CDL-CVI selected the reference number of clusters more often and reached higher Adjusted Rand Index (ARI) values than the conventional CVIs we tested, without an additional kernel preprocessing stage. On image benchmarks (MNIST, CIFAR-10, STL-10) clustered from frozen unsupervised embeddings, CDL-CVI returned cluster numbers close to the reference class counts across K-means, DBSCAN, and spectral clustering in the reported trials.

Sparse high-dimensional representations are conducive to uncovering nontrivial structures in unsupervised exploration of data. Such a representation can deal with the dense connectivity in graphs relevant to community detection problems. However, sparse high-dimensional representations are capable of doing more, including manifold tiling and feature learning. Conventional algorithms optimize in the space of computationally intractable completely positive matrices or relax the problem to the space of doubly nonnegative matrices that scale with sample size in a way rendering them impractical for large data sets. Some of these methods also impose a row sum constraint, such as double stochasticity. Row sum constraints have the added advantage of being shift-invariant, in the context of manifold tiling. Constraints on the row sum of output similarity matrices require nontrivial online learning rules. Addressing these needs, we propose a versatile online biologically plausible learning algorithm capable of learning sparse shift-invariant representations, useful for clustering, manifold tiling, or sparse coding, depending on the data structure.

Clustering is an unsupervised technique for grouping data points by similarity. While explainability methods exist for supervised machine learning, they are not directly applicable to clustering, making it challenging to understand cluster assignments. This interpretability gap is particularly evident in the popular density-based method DBSCAN, which assigns points as inliers (cluster members in dense regions) or outliers (noise points in sparse regions). DBSCAN does not provide insight into why a particular point receives its assignment or whether its assignment is robust to small changes in the data. To address the lack of explainability, we introduce ExDBSCAN, a density-aware, post-hoc explanation method. ExDBSCAN offers actionable counterfactual explanations, with theoretical guarantees for validity. It generates multiple counterfactuals using a density connected weighted graph, adopting a physics-inspired model that repels counterfactual candidates from one another (diversity), while pulling them toward the instance to explain (proximity). Empirical evaluation on 30 tabular datasets comparing against four baselines shows that ExDBSCAN outperforms all baselines while attaining perfect validity and retrieving diverse, proximal counterfactuals.

Cluster analysis is a widely applied machine learning technique to understand the existing patterns in the population of gamma-ray bursts (GRBs), in order to explore their physical sources. In the present scenario, the number of clusters corresponding to differentiable groups is still under conflict, in spite of numerous attempts with the state-of-the-art clustering procedures. This crucial unknown parameter needs to be evaluated, either directly or indirectly in terms of other tuning parameters, to produce the clusters in GRBs through implementation of an appropriate clustering algorithm. While most of the applied algorithms reached two physically explained groups of merger and collapsar predominated by the short and long bursts respectively, other statistical approaches violated this binary partition. However, physical establishment of any additional cluster(s) is not yet confirmed. Therefore, we propose a new algorithm, from a different stream of clustering referred to as `completely parameter-free', which carries out the classification of GRBs in a manner that has not been tried so far. It indicates two main groups, of short and long duration bursts from the BATSE sample, compatible with the merger-collapsar theory.

Clustering is a fundamental problem in data science with a long-standing research history, yielding numerous insightful algorithms. Despite this progress, a systematic and large-scale empirical evaluation that jointly considers conventional algorithms, deep learning-based methods, and recent foundation model-based clustering remains largely absent, leading to limited guidance on algorithm selection and deployment. To address this gap, we introduce CLUBench, a comprehensive clustering benchmark comprising 24 algorithms of diverse principles evaluated on 131 datasets across tabular, text, and image data, involving 178,815 experiments. Importantly, our analyses of (i) the impact of hyperparameter tuning,(ii) the impact of data types and characteristics,(iii) the impact of pretrained embeddings,(iv) large language model-based clustering,(v) the similarity of algorithms, and (vi) the low-rank structures of performance matrices, yield meaningful insights and promising pathways for clustering research. For instance, our study reveals that: 1) All evaluated deep clustering methods do not exhibit a significant advantage compared with the top-performing conventional clustering algorithms (e.g., KMeans, SpeClu) in terms of average performance; 2) For image and text clustering tasks, combining pretrained embeddings with conventional clustering algorithms (e.g., KMeans, SpeClu) offers effective and efficient clustering; 3) Clustering remains a challenging and nontrivial problem, even in the era of increasingly dominant foundation models. Moreover, we propose to use the low-rank structure in cross-model performance matrices to efficiently approximate the overall performance evaluation in practical applications. We further demonstrate the feasibility of model selection based on the performance matrices across all hyperparameter configurations.

Unsupervised learning methods -- topic modeling, partition-based and density-based clustering -- produce data groupings without human guidance, yet choosing and evaluating those groupings should not itself be unsupervised. We present \emph{SmartIterator}(SI), a visual analytics approach that treats the full sequence of grouping results across a parameter sweep as a first-class analytical object. For each method family, SI provides a structured six-phase workflow that guides the analyst through systematic exploration of grouping results -- from quality-metric overview through transition-stability assessment, membership-confidence evaluation, content and context inspection, and recurrent-archetype verification to an informed decision -- building cumulative understanding of data structure along the way. The workflows are operationalized through \emph{IteraScope}(IS), a coordinated visual display combining quality-metric charts with semantic color encoding, a 1D group embedding with Sankey-style transition flows and violin plots of membership confidence, a 2D group embedding with HDBSCAN-detected recurrent archetypes that highlights iterations capturing all persistent patterns, and domain-specific linked views for contextualized interpretation. We demonstrate the three workflows on: (1)~simulated social-media messages from the VAST Challenge 2011 (density-based clustering, validated against ground truth), (2)~EU population statistics across ${\sim}1\,500$ NUTS-3 regions (partition-based clustering), and (3)~30 years of IEEE VIS papers (NMF topic modeling). The workflows constitute the main contribution: they provide actionable, method-specific guidance for navigating parameter spaces, studying how data structure evolves across configurations, and grounding analytical understanding in domain context -- yielding knowledge about the data that no single ``best'' result can provide.