Clustering

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Clustering seeks useful groupings when labels are absent or incomplete, helping reveal structure in data such as text, images, graphs, time series, and scientific measurements. Methods include centroid-based k-means, density and hierarchical clustering, graph and spectral methods, mixture models, and newer approaches that learn embeddings or use optimal transport; fairness, privacy, streaming, and federated settings add further constraints. Work also studies how to choose the number of clusters and assess stability, uncertainty, interpretability, and statistical significance. No single method works best across data types: deep methods do not consistently beat strong conventional algorithms, and reliable validation remains a central challenge.

Latest papers

345 papers31 papers in the last four weeks, up 11% on the four weeks before. 0.2% of all new papers.

Apr 13, 2026

Melodic contour does not cluster: Reconsidering contour typology

How to describe the shape of a melodic phrase? Scholars have often relied on typologies with a small set of contour types. We question their adequacy: we find no evidence that phrase contours cluster into discrete types, neither in German or Chinese folksongs, nor in Gregorian chant. The test for clustering we propose applies the dist-dip test of multimodality after a UMAP dimensionality reduction. The test correctly identifies clustering in a synthetic dataset, but not in actual phrase contours. These results raise problems for discrete typologies. In particular, type frequencies may be unreliable, as we see with Huron's typology. We also show how a recent finding of four contour shapes may be an artefact of the analysis. Our findings suggest that melodic contour is best seen as a continuous phenomenon.

Bas Cornelissen, Willem Zuidema, John Ashley Burgoyne +1

Institute for Logic, Language and Computation, University of Amsterdam

Apr 13, 2026

Distributionally Robust K-Means Clustering

K-means clustering is a workhorse of unsupervised learning, but it is notoriously brittle to outliers, distribution shifts, and limited sample sizes. Viewing k-means as Lloyd--Max quantization of the empirical distribution, we develop a distributionally robust variant that protects against such pathologies. We posit that the unknown population distribution lies within a Wasserstein-2 ball around the empirical distribution. In this setting, one seeks cluster centers that minimize the worst-case expected squared distance over this ambiguity set, leading to a minimax formulation. A tractable dual yields a soft-clustering scheme that replaces hard assignments with smoothly weighted ones. We propose an efficient block coordinate descent algorithm with provable monotonic decrease and local linear convergence. Experiments on standard benchmarks and large-scale synthetic data demonstrate substantial gains in outlier detection and robustness to noise.

Vikrant Malik, Taylan Kargin, Babak Hassibi

Department of Electrical Engineering, California Institute of Technology, Pasadena, CA 91125 USA. · California Institute of Technology, Pasadena, CA 91125 USA · Massachusetts Institute of Technology, Cambridge, MA 02139 USA.

Clustering Distribution Shift Robustness Wasserstein Distributionally Robust Optimization

Apr 13, 2026

Beyond Statistical Co-occurrence: Unlocking Intrinsic Semantics for Tabular Data Clustering

Deep Clustering (DC) has emerged as a powerful tool for tabular data analysis in real-world domains like finance and healthcare. However, most existing methods rely on data-level statistical co-occurrence to infer the latent metric space, often overlooking the intrinsic semantic knowledge encapsulated in feature names and values. As a result, semantically related concepts like Flu' and Cold' are often treated as symbolic tokens, causing conceptually related samples to be isolated. To bridge the gap between dataset-specific statistics and intrinsic semantic knowledge, this paper proposes Tabular-Augmented Contrastive Clustering (TagCC), a novel framework that anchors statistical tabular representations to open-world textual concepts. Specifically, TagCC utilizes Large Language Models (LLMs) to distill underlying data semantics into textual anchors via semantic-aware transformation. Through Contrastive Learning (CL), the framework enriches the statistical tabular representations with the open-world semantics encapsulated in these anchors. This CL framework is jointly optimized with a clustering objective, ensuring that the learned representations are both semantically coherent and clustering-friendly. Extensive experiments on benchmark datasets demonstrate that TagCC significantly outperforms its counterparts.

Mingjie Zhao, Yunfan Zhang, Yiqun Zhang +1

Department of Computer Science, Hong Kong Baptist University, Hong Kong, China · Department of Computer Science, Guangdong University of Technology, Guangzhou, China

Clustering Deep Clustering Tabular Representation Learning Contrastive Learning

Apr 11, 2026

A Structured Clustering Approach for Inducing Media Narratives

Media narratives wield tremendous power in shaping public opinion, yet computational approaches struggle to capture the nuanced storytelling structures that communication theory emphasizes as central to how meaning is constructed. Existing approaches either miss subtle narrative patterns through coarse-grained analysis or require domain-specific taxonomies that limit scalability. To bridge this gap, we present a framework for inducing rich narrative schemas by jointly modeling events and characters via structured clustering. Our approach produces explainable narrative schemas that align with established framing theory while scaling to large corpora without exhaustive manual annotation.

Rohan Das, Advait Deshmukh, Alexandria Leto +3

University of Colorado Boulder · Independent Researcher

Clustering Computational Social Science

Apr 9, 2026

The Condition-Number Principle for Prototype Clustering

We develop a geometric framework that links objective accuracy to structural recovery in prototype-based clustering. The analysis is algorithm-agnostic and applies to a broad class of admissible loss functions. We define a clustering condition number that compares within-cluster scale to the minimum loss increase required to move a point across a cluster boundary. When this quantity is small, any solution with a small suboptimality gap must also have a small misclassification error relative to a benchmark partition. The framework also clarifies a fundamental trade-off between robustness and sensitivity to cluster imbalance, leading to sharp phase transitions for exact recovery under different objectives. The guarantees are deterministic and non-asymptotic, and they separate the role of algorithmic accuracy from the intrinsic geometric difficulty of the instance. We further show that errors concentrate near cluster boundaries and that sufficiently deep cluster cores are recovered exactly under strengthened local margins. Together, these results provide a geometric principle for interpreting low objective values as reliable evidence of meaningful clustering structure.

Romano Li, Jianfei Cao

Department of Economics, Duke University · Department of Economics, Northeastern University

Apr 8, 2026

On the Uphill Battle of Image frequency Analysis

This work is a follow up on the newly proposed clustering algorithm called The Inverse Square Mean Shift Algorithm. In this paper a special case of algorithm for dealing with non-homogenous data is formulated and the three dimensional Fast Fourier Transform of images is investigated with the aim of finding hidden patterns.

Nader Bazyari, Hedieh Sajedi

Department of Computer Science, School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran

Frequency-Domain Image Processing Image Clustering Clustering

Apr 8, 2026

Reasoning-Based Refinement of Unsupervised Text Clusters with LLMs

Unsupervised methods are widely used to induce latent semantic structure from large text collections, yet their outputs often contain incoherent, redundant, or poorly grounded clusters that are difficult to validate without labeled data. We propose a reasoning-based refinement framework that leverages large language models (LLMs) not as embedding generators, but as semantic judges that validate and restructure the outputs of arbitrary unsupervised clustering algorithms. Our framework introduces three reasoning stages: (i) coherence verification, where LLMs assess whether cluster summaries are supported by their member texts; (ii) redundancy adjudication, where candidate clusters are merged or rejected based on semantic overlap; and (iii) label grounding, where clusters are assigned interpretable labels through a two-stage process that generates and consolidates semantically similar labels in a fully unsupervised manner. This design decouples representation learning from structural validation and mitigates the common failure modes of embedding-only approaches. We evaluate the framework in real-world social media corpora from two platforms with distinct interaction models, demonstrating consistent improvements in cluster coherence and human-aligned labeling quality over classical topic models and recent representation-based baselines. Human evaluation shows strong agreement with LLM-generated labels, despite the absence of gold-standard annotations. We further conduct robustness analysis under matched temporal and volume conditions to assess cross-platform stability. Beyond empirical gains, our results suggest that LLM-based reasoning can serve as a general mechanism for validating and refining unsupervised semantic structure, enabling more reliable and interpretable analysis of large text collections without supervision.

Tunazzina Islam

Department of Computer Science, Purdue University, West Lafayette, IN 47907

Clustering Unsupervised Clustering

Apr 8, 2026

Lumbermark: Resistant Clustering by Chopping Up Mutual Reachability Minimum Spanning Trees

We introduce Lumbermark, a robust divisive clustering algorithm capable of detecting clusters of varying sizes, densities, and shapes. Lumbermark iteratively chops off large limbs connected by protruding segments of a dataset's mutual reachability minimum spanning tree. The use of mutual reachability distances smoothens the data distribution and decreases the influence of low-density objects, such as noise points between clusters or outliers at their peripheries. The algorithm can be viewed as an alternative to HDBSCAN that produces partitions with user-specified sizes. A fast, easy-to-use implementation of the new method is available in the open-source 'lumbermark' package for Python and R. We show that Lumbermark performs well on benchmark data and hope it will prove useful to data scientists and practitioners across different fields.

Marek Gagolewski

Warsaw University of Technology, Faculty of Mathematics and Information Science, ul. Koszykowa 75, 00-662 Warsaw, Poland · Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland

Density-Based Clustering Clustering Hierarchical Clustering

Apr 8, 2026

Mining Electronic Health Records to Investigate Effectiveness of Ensemble Deep Clustering

In electronic health records (EHRs), clustering patients and distinguishing disease subtypes are key tasks to elucidate pathophysiology and aid clinical decision-making. However, clustering in healthcare informatics is still based on traditional methods, especially K-means, and has achieved limited success when applied to embedding representations learned by autoencoders as hybrid methods. This paper investigates the effectiveness of traditional, hybrid, and deep learning methods in heart failure patient cohorts using real EHR data from the All of Us Research Program. Traditional clustering methods perform robustly because deep learning approaches are specifically designed for image clustering, a task that differs substantially from the tabular EHR data setting. To address the shortcomings of deep clustering, we introduce an ensemble-based deep clustering approach that aggregates cluster assignments obtained from multiple embedding dimensions, rather than relying on a single fixed embedding space. When combined with traditional clustering in a novel ensemble framework, the proposed ensemble embedding for deep clustering delivers the best overall performance ranking across 14 diverse clustering methods and multiple patient cohorts. This paper underscores the importance of biological sex-specific clustering of EHR data and the advantages of combining traditional and deep clustering approaches over a single method.

Manar D. Samad, Yina Hou, Shrabani Ghosh

Department of Computer Science Tennessee State University Nashville, TN, USA

Clustering Deep Clustering Electronic Health Records

Apr 8, 2026

A Data-Informed Variational Clustering Framework for Noisy High-Dimensional Data

Clustering in high-dimensional settings with severe feature noise remains challenging, especially when only a small subset of dimensions is informative and the final number of clusters is not specified in advance. In such regimes, partition recovery, feature relevance learning, and structural adaptation are tightly coupled, and standard likelihood-based methods can become unstable or overly sensitive to noisy dimensions. We propose DIVI, a data-informed variational clustering framework that combines global feature gating with split-based adaptive structure growth. DIVI uses informative prior initialization to stabilize optimization, learns feature relevance in a differentiable manner, and expands model complexity only when local diagnostics indicate underfit. Beyond clustering performance, we also examine runtime scalability and parameter sensitivity in order to clarify the computational and practical behavior of the framework. Empirically, we find that DIVI performs competitively under severe feature noise, remains computationally feasible, and yields interpretable feature-gating behavior, while also exhibiting conservative growth and identifiable failure regimes in challenging settings. Overall, DIVI is best viewed as a practical variational clustering framework for noisy high-dimensional data rather than as a fully Bayesian generative solution.

Wan Ping Chen

Department of Mathematics, Fu Jen Catholic University, Taipei, Taiwan, No. 510 Zhongzheng Rd., Xinzhuang Dist., New Taipei City, 242062, Taiwan

Clustering Unsupervised Clustering

Apr 7, 2026

Weight-Informed Self-Explaining Clustering for Mixed-Type Tabular Data

Clustering mixed-type tabular data is fundamental for exploratory analysis, yet remains challenging due to misaligned numerical-categorical representations, uneven and context-dependent feature relevance, and disconnected and post-hoc explanation from the clustering process. We propose WISE, a Weight-Informed Self-Explaining framework that unifies representation, feature weighting, clustering, and interpretation in a fully unsupervised and transparent pipeline. WISE introduces Binary Encoding with Padding (BEP) to align heterogeneous features in a unified sparse space, a Leave-One-Feature-Out (LOFO) strategy to sense multiple high-quality and diverse feature-weighting views, and a two-stage weight-aware clustering procedure to aggregate alternative semantic partitions. To ensure intrinsic interpretability, we further develop Discriminative FreqItems (DFI), which yields feature-level explanations that are consistent from instances to clusters with an additive decomposition guarantee. Extensive experiments on six real-world datasets demonstrate that WISE consistently outperforms classical and neural baselines in clustering quality while remaining efficient, and produces faithful, human-interpretable explanations grounded in the same primitives that drive clustering.

Lehao Li, Qiang Huang, Yihao Ang +3

School of Computing, National University of Singapore, Singapore · School of Intelligence Science and Engineering, Harbin Institute of Technology (Shenzhen), China

Apr 7, 2026

Individual-heterogeneous sub-Gaussian Mixture Models

The classical Gaussian mixture model assumes homogeneity within clusters, an assumption that often fails in real-world data where observations naturally exhibit varying scales or intensities. To address this, we introduce the individual-heterogeneous sub-Gaussian mixture model, a flexible framework that assigns each observation its own heterogeneity parameter, thereby explicitly capturing the heterogeneity inherent in practical applications. Built upon this model, we propose an efficient spectral method that provably achieves exact recovery of the true cluster labels under mild separation conditions, even in high-dimensional settings where the number of features far exceeds the number of samples. Numerical experiments on both synthetic and real data demonstrate that our method consistently outperforms existing clustering algorithms, including those designed for classical Gaussian mixture models.

Huan Qing

School of Economics and Finance, Chongqing University of Technology, Chongqing, 400054, China

Clustering Gaussian Mixture Models Latent Variable Models Spectral Clustering

Apr 5, 2026

CavMerge: Merging K-means Based on Local Log-Concavity

K-means clustering, a classic and widely-used clustering technique, is known to exhibit suboptimal performance when applied to non-linearly separable data. Numerous adjustments and modifications have been proposed to address this issue, including methods that merge K-means results from a relatively large K to obtain a final cluster assignment. However, existing methods of this nature often encounter computational inefficiencies and suffer from hyperparameter tuning. Here we present CavMerge, a novel K-means merging algorithm that is intuitive, free of parameter tuning, and computationally efficient. Operating under minimal local distributional assumptions, our algorithm demonstrates strong consistency and rapid convergence guarantees. Empirical studies on various simulated and real datasets demonstrate that our method yields more reliable clusters in comparison to current state-of-the-art algorithms.

Zhili Qiao, Wangqian Ju, Peng Liu

Department of Statistics, Iowa State University

Clustering Unsupervised Clustering

Apr 5, 2026

Biconvex Biclustering

This article proposes a biconvex modification to convex biclustering in order to improve its performance in high-dimensional settings. In contrast to heuristics that discard a subset of noisy features a priori, our method jointly learns and accordingly weighs informative features while discovering biclusters. Moreover, the method is adaptive to the data, and is accompanied by an efficient algorithm based on proximal alternating minimization, complete with detailed guidance on hyperparameter tuning and efficient solutions to optimization subproblems. These contributions are theoretically grounded; we establish finite-sample bounds on the objective function under sub-Gaussian errors, and generalize these guarantees to cases where input affinities need not be uniform. Extensive simulation results reveal our method consistently recovers underlying biclusters while weighing and selecting features appropriately, outperforming peer methods. An application to a gene microarray dataset of lymphoma samples recovers biclusters matching an underlying classification, while giving additional interpretation to the mRNA samples via the column groupings and fitted weights.

Sam Rosen, Eric C. Chi, Jason Xu

Department of Statistical Science, Duke University · School of Statistics, University of Minnesota · Department of Biostatistics, University of California Los Angeles

Clustering Feature Selection

Apr 3, 2026

PRISM: LLM-Guided Semantic Clustering for High-Precision Topics

In this paper, we propose Precision-Informed Semantic Modeling (PRISM), a structured topic modeling framework combining the benefits of rich representations captured by LLMs with the low cost and interpretability of latent semantic clustering methods. PRISM fine-tunes a sentence encoding model using a sparse set of LLM- provided labels on samples drawn from some corpus of interest. We segment this embedding space with thresholded clustering, yielding clusters that separate closely related topics within some narrow domain. Across multiple corpora, PRISM improves topic separability over state-of-the-art local topic models and even over clustering on large, frontier embedding models while requiring only a small number of LLM queries to train. This work contributes to several research streams by providing (i) a student-teacher pipeline to distill sparse LLM supervision into a lightweight model for topic discovery; (ii) an analysis of the efficacy of sampling strategies to improve local geometry for cluster separability; and (iii) an effective approach for web-scale text analysis, enabling researchers and practitioners to track nuanced claims and subtopics online with an interpretable, locally deployable framework.

Connor Douglas, Utkucan Balci, Joseph Aylett-Bullock

New York University New York, NY, USA · Binghamton University Binghamton, NY, USA · United Nations New York, NY, USA

Semantic Clustering Topic Modeling Clustering Knowledge Distillation

Apr 2, 2026

A Novel Theoretical Analysis for Clustering Heteroscedastic Gaussian Data without Knowledge of the Number of Clusters

This paper addresses the problem of clustering measurement vectors that are heteroscedastic in that they can have different covariance matrices. From the assumption that the measurement vectors within a given cluster are Gaussian distributed with possibly different and unknown covariant matrices around the cluster centroid, we introduce a novel cost function to estimate the centroids. The zeros of the gradient of this cost function turn out to be the fixed-points of a certain function. As such, the approach generalizes the methodology employed to derive the existing Mean-Shift algorithm. But as a main and novel theoretical result compared to Mean-Shift, this paper shows that the sole fixed-points of the identified function tend to be the cluster centroids if both the number of measurements per cluster and the distances between centroids are large enough. As a second contribution, this paper introduces the Wald kernel for clustering. This kernel is defined as the p-value of the Wald hypothesis test for testing the mean of a Gaussian. As such, the Wald kernel measures the plausibility that a measurement vector belongs to a given cluster and it scales better with the dimension of the measurement vectors than the usual Gaussian kernel. Finally, the proposed theoretical framework allows us to derive a new clustering algorithm called CENTRE-X that works by estimating the fixed-points of the identified function. As Mean-Shift, CENTRE-X requires no prior knowledge of the number of clusters. It relies on a Wald hypothesis test to significantly reduce the number of fixed points to calculate compared to the Mean-Shift algorithm, thus resulting in a clear gain in complexity. Simulation results on synthetic and real data sets show that CENTRE-X has comparable or better performance than standard clustering algorithms K-means and Mean-Shift, even when the covariance matrices are not perfectly known.

Dominique Pastor, Elsa Dupraz, Ismail Hbilou +1

Lab-STICC, IMT Atlantique, 29238 Brest, France · OPTI’SEA 23 rue du Bourgneuf 29300 Quimperlé, France

Clustering Unsupervised Clustering Kernel Methods

Apr 2, 2026

DDCL: Deep Dual Competitive Learning: A Differentiable End-to-End Framework for Unsupervised Prototype-Based Representation Learning

A persistent structural weakness in deep clustering is the disconnect between feature learning and cluster assignment. Most architectures invoke an external clustering step, typically k-means, to produce pseudo-labels that guide training, preventing the backbone from directly optimising for cluster quality. This paper introduces Deep Dual Competitive Learning (DDCL), the first fully differentiable end-to-end framework for unsupervised prototype-based representation learning. The core contribution is architectural: the external k-means is replaced by an internal Dual Competitive Layer (DCL) that generates prototypes as native differentiable outputs of the network. This single inversion makes the complete pipeline, from backbone feature extraction through prototype generation to soft cluster assignment, trainable by backpropagation through a single unified loss, with no Lloyd iterations, no pseudo-label discretisation, and no external clustering step. To ground the framework theoretically, the paper derives an exact algebraic decomposition of the soft quantisation loss into a simplex-constrained reconstruction error and a non-negative weighted prototype variance term. This identity reveals a self-regulating mechanism built into the loss geometry: the gradient of the variance term acts as an implicit separation force that resists prototype collapse without any auxiliary objective, and leads to a global Lyapunov stability theorem for the reduced frozen-encoder system. Six blocks of controlled experiments validate each structural prediction. The decomposition identity holds with zero violations across more than one hundred thousand training epochs; the negative feedback cycle is confirmed with Pearson -0.98; with a jointly trained backbone, DDCL outperforms its non-differentiable ablation by 65% in clustering accuracy and DeepCluster end-to-end by 122%.

Giansalvo Cirrincione

Lab. LTI, Université de Picardie Jules Verne, Amiens, France

Clustering Deep Clustering Unsupervised Representation Learning Representation Learning

Mar 31, 2026

Deep Image Clustering Based on Curriculum Learning and Density Information

Image clustering is one of the crucial techniques in multimedia analytics and knowledge discovery. Recently, the Deep clustering method (DC), characterized by its ability to perform feature learning and cluster assignment jointly, surpasses the performance of traditional ones on image data. However, existing methods rarely consider the role of model learning strategies in improving the robustness and performance of clustering complex image data. Furthermore, most approaches rely solely on point-to-point distances to cluster centers for partitioning the latent representations, resulting in error accumulation throughout the iterative process. In this paper, we propose a robust image clustering method (IDCL) which, to our knowledge for the first time, introduces a model training strategy using density information into image clustering. Specifically, we design a curriculum learning scheme grounded in the density information of input data, with a more reasonable learning pace. Moreover, we employ the density core rather than the individual cluster center to guide the cluster assignment. Finally, extensive comparisons with state-of-the-art clustering approaches on benchmark datasets demonstrate the superiority of the proposed method, including robustness, rapid convergence, and flexibility in terms of data scale, number of clusters, and image context.

Haiyang Zheng, Ruilin Zhang, Hongpeng Wang

Harbin Institute of Technology, Shenzhen, Shenzhen, China · Harbin Institute of Technology, Shenzhen & Peng Cheng Laboratory, Shenzhen, China

Density-Based Clustering Clustering Image Clustering Deep Clustering Curriculum Learning

Mar 28, 2026

Kempe Swap K-Means: A Scalable Near-Optimal Solution for Semi-Supervised Clustering

This paper presents a novel centroid-based heuristic algorithm, termed Kempe Swap K-Means, for constrained clustering under rigid must-link (ML) and cannot-link (CL) constraints. The algorithm employs a dual-phase iterative process: an assignment step that utilizes Kempe chain swaps to refine current clustering in the constrained solution space and a centroid update step that computes optimal cluster centroids. To enhance global search capabilities and avoid local optima, the framework incorporates controlled perturbations during the update phase. Empirical evaluations demonstrate that the proposed method achieves near-optimal partitions while maintaining high computational efficiency and scalability. The results indicate that Kempe Swap K-Means consistently outperforms state-of-the-art benchmarks in both clustering accuracy and algorithmic efficiency for large-scale datasets.

Yuxuan Ren, Shijie Deng

School of Industrial and Systems Engineering Georgia Institute of Technology, USA

Clustering Semi-Supervised Learning

Mar 26, 2026

Cluster-Adaptive Feature Extraction and its Theoretical Foundation with Minkowski Weighted k-Means

The Minkowski weighted

k

-means (

mwk

-means) algorithm extends classical

k

-means by incorporating feature weights and a Minkowski distance. We first show that the

mwk

-means objective can be expressed as a power-mean aggregation of within-cluster dispersions, with the order determined by the Minkowski exponent

p

. This formulation reveals how

p

controls the transition between selective and uniform use of features. Using this representation, we derive bounds for the objective function and characterise the structure of the feature weights, showing that they depend only on relative dispersion and follow a power-law relationship with dispersion ratios. This leads to explicit guarantees on the suppression of high-dispersion features, and we establish convergence of the algorithm. Building on these theoretical results, we introduce Cluster-Adaptive Feature Extraction (CAFE), a method that uses the

mwk

-means feature weights to rescale the data prior to unsupervised feature extraction. We prove that this rescaling reverses the within-cluster dispersion ordering, suppressing noisy features and amplifying informative ones. Numerous experiments conducted under controlled within-cluster noise show that CAFE consistently improves the results of traditional feature extraction methods.

Renato Cordeiro de Amorim, Vladimir Makarenkov

School of Computer Science and Electronic Engineering, University of Essex, Wivenhoe, UK. · D´epartement d’informatique, Universit´e du Qu´ebec `a Montr´eal, C.P. 8888 succ. Centre-Ville, Montreal (QC) H3C 3P8 Canada. · Mila - Quebec AI Institute, Montreal, QC, Canada.

Clustering Unsupervised Clustering Unsupervised Representation Learning

Mar 25, 2026

Language-Assisted Image Clustering Guided by Discriminative Relational Signals and Adaptive Semantic Centers

Language-Assisted Image Clustering (LAIC) augments the input images with additional texts with the help of vision-language models (VLMs) to promote clustering performance. Despite recent progress, existing LAIC methods often overlook two issues: (i) textual features constructed for each image are highly similar, leading to weak inter-class discriminability; (ii) the clustering step is restricted to pre-built image-text alignments, limiting the potential for better utilization of the text modality. To address these issues, we propose a new LAIC framework with two complementary components. First, we exploit cross-modal relations to produce more discriminative self-supervision signals for clustering, as it compatible with most VLMs training mechanisms. Second, we learn category-wise continuous semantic centers via prompt learning to produce the final clustering assignments. Extensive experiments on eight benchmark datasets demonstrate that our method achieves an average improvement of 2.6% over state-of-the-art methods, and the learned semantic centers exhibit strong interpretability. Code is available in the supplementary material.

Jun Ma, Xu Zhang, Zhengxing Jiao +4

School of Computer Science and Engineering, Southeast University, Nanjing, China · School of Computing Information Sciences, Saint Francis University, Hong Kong, China · Department of Computer Science, City University of Hong Kong, Hong Kong, China

Image Clustering Clustering Semantic Clustering

Mar 25, 2026

Granular Ball Guided Stable Latent Domain Discovery for Domain-General Crowd Counting

Single-source domain generalization for crowd counting is highly challenging because a single labeled source domain may contain heterogeneous latent domains, while unseen target domains often exhibit severe distribution shifts. A central issue is stable latent domain discovery: directly performing flat clustering on evolving sample-level latent features is easily disturbed by feature noise, outliers, and representation drift, leading to unreliable pseudo-domain assignments and weakened domain-structured learning. To address this problem, we propose a granular ball guided stable latent domain discovery framework for domain-general crowd counting. The proposed method first groups samples into compact local granular balls and then clusters granular ball centers as representatives to infer pseudo-domains, thereby converting direct sample-level clustering into a hierarchical representative-based clustering process. This design produces more stable and semantically consistent pseudo-domain assignments. On top of the discovered latent domains, we develop a two-branch learning framework that improves transferable semantic representations via semantic codebook re-encoding and captures domain-specific appearance variations through a style branch, thereby alleviating semantic--style entanglement under domain shifts. Extensive experiments on ShanghaiTech A/B, UCF_QNRF, and NWPU-Crowd under a strict no-adaptation protocol verify the effectiveness of the proposed method and show strong generalization ability, especially in transfer settings with large domain gaps.

Fan Chen, Shuyin Xia, Yi Wang

Chongqing University of Posts and Telecommunications, Chongqing, China · Chongqing Ant Consumer Finance Co., Ltd., Chongqing, China

Crowd Counting Domain Generalization Cross-Domain Generalization Clustering

Mar 24, 2026

Contrastive Metric Learning for Point Cloud Segmentation in Highly Granular Detectors

We propose a novel clustering approach for point-cloud segmentation based on supervised contrastive metric learning (CML). Rather than predicting cluster assignments or object-centric variables, the method learns a latent representation in which points belonging to the same object are embedded nearby while unrelated points are separated. Clusters are then reconstructed using a density-based readout in the learned metric space, decoupling representation learning from cluster formation and enabling flexible inference. The approach is evaluated on simulated data from a highly granular calorimeter, where the task is to separate highly overlapping particle showers represented as sets of calorimeter hits. A direct comparison with object condensation (OC) is performed using identical graph neural network backbones and equal latent dimensionality, isolating the effect of the learning objective. The CML method produces a more stable and separable embedding geometry for both electromagnetic and hadronic particle showers, leading to improved local neighbourhood consistency, a more reliable separation of overlapping showers, and better generalization when extrapolating to unseen multiplicities and energies. This translates directly into higher reconstruction efficiency and purity, particularly in high-multiplicity regimes, as well as improved energy resolution. In mixed-particle environments, CML maintains strong performance, suggesting robust learning of the shower topology, while OC exhibits significant degradation. These results demonstrate that similarity-based representation learning combined with density-based aggregation is a promising alternative to object-centric approaches for point cloud segmentation in highly granular detectors.

Max Marriott-Clarke, Lazar Novakovic, Elizabeth Ratzer +3

Blackett Laboratory, Imperial College London, UK · Department of Physics & Astronomy, Brown University, USA · Brown Center for Theoretical Physics and Innovation (BCTPI), Brown University, USA

Density-Based Clustering 3D Point Cloud Segmentation Clustering Supervised Contrastive Learning Metric Learning

Mar 24, 2026

The Mass Agreement Score: A Point-centric Measure of Cluster Size Consistency

In clustering, strong dominance in the size of a particular cluster is often undesirable, motivating a measure of cluster size uniformity that can be used to filter such partitions. A basic requirement of such a measure is stability: partitions that differ only slightly in their point assignments should receive similar uniformity scores. A difficulty arises because cluster labels are not fixed objects; algorithms may produce different numbers of labels even when the underlying point distribution changes very little. Measures defined directly over labels can therefore become unstable under label-count perturbations. I introduce the Mass Agreement Score (MAS), a point-centric metric bounded in [0, 1] that evaluates the consistency of expected cluster size as measured from the perspective of points in each cluster. Its construction yields fragment robustness by design, assigning similar scores to partitions with similar bulk structure while remaining sensitive to genuine redistribution of cluster mass.

Randolph Wiredu-Aidoo

Mar 23, 2026

TDEC: Deep Embedded Image Clustering with Transformer and Distribution Information

Image clustering is a crucial but challenging task in multimedia machine learning. Recently the combination of clustering with deep learning has achieved promising performance against conventional methods on high-dimensional image data. Unfortunately, existing deep clustering methods (DC) often ignore the importance of information fusion with a global perception field among different image regions on clustering images, especially complex ones. Additionally, the learned features are usually clustering-unfriendly in terms of dimensionality and are based only on simple distance information for the clustering. In this regard, we propose a deep embedded image clustering TDEC, which for the first time to our knowledge, jointly considers feature representation, dimensional preference, and robust assignment for image clustering. Specifically, we introduce the Transformer to form a novel module T-Encoder to learn discriminative features with global dependency while using the Dim-Reduction block to build a friendly low-dimensional space favoring clustering. Moreover, the distribution information of embedded features is considered in the clustering process to provide reliable supervised signals for joint training. Our method is robust and allows for more flexibility in data size, the number of clusters, and the context complexity. More importantly, the clustering performance of TDEC is much higher than recent competitors. Extensive experiments with state-of-the-art approaches on complex datasets show the superiority of TDEC.

Ruilin Zhang, Haiyang Zheng, Hongpeng Wang

Harbin Institute of Technology, Shenzhen, Shenzhen, China · Harbin Institute of Technology, Shenzhen, & Peng Cheng Laboratory, Shenzhen, China

Clustering Image Clustering Deep Clustering

Mar 23, 2026

CNMBI: Determining the Number of Clusters Using Center Pairwise Matching and Boundary Filtering

One of the main challenges in data mining is choosing the optimal number of clusters without prior information. Notably, existing methods are usually in the philosophy of cluster validation and hence have underlying assumptions on data distribution, which prevents their application to complex data such as large-scale images and high-dimensional data from the real world. In this regard, we propose an approach named CNMBI. Leveraging the distribution information inherent in the data space, we map the target task as a dynamic comparison process between cluster centers regarding positional behavior, without relying on the complete clustering results and designing the complex validity index as before. Bipartite graph theory is then employed to efficiently model this process. Additionally, we find that different samples have different confidence levels and thereby actively remove low-confidence ones, which is, for the first time to our knowledge, considered in cluster number determination. CNMBI is robust and allows for more flexibility in the dimension and shape of the target data (e.g., CIFAR-10 and STL-10). Extensive comparison studies with state-of-the-art competitors on various challenging datasets demonstrate the superiority of our method.

Ruilin Zhang, Haiyang Zheng, Hongpeng Wang

Harbin Institute of Technology, Shenzhen, Shenzhen, China · Peng Cheng Laboratory, Shenzhen, China

Cluster Number Estimation Clustering

Mar 23, 2026

Feature Incremental Clustering with Generalization Bounds

In many learning systems, such as activity recognition systems, as new data collection methods continue to emerge in various dynamic environmental applications, the attributes of instances accumulate incrementally, with data being stored in gradually expanding feature spaces. How to design theoretically guaranteed algorithms to effectively cluster this special type of data stream, commonly referred to as activity recognition, remains unexplored. Compared to traditional scenarios, we will face at least two fundamental questions in this feature incremental scenario. (i) How to design preliminary and effective algorithms to address the feature incremental clustering problem? (ii) How to analyze the generalization bounds for the proposed algorithms and under what conditions do these algorithms provide a strong generalization guarantee? To address these problems, by tailoring the most common clustering algorithm, i.e.,

k

-means, as an example, we propose four types of Feature Incremental Clustering (FIC) algorithms corresponding to different situations of data access: Feature Tailoring (FT), Data Reconstruction (DR), Data Adaptation (DA), and Model Reuse (MR), abbreviated as FIC-FT, FIC-DR, FIC-DA, and FIC-MR. Subsequently, we offer a detailed analysis of the generalization error bounds for these four algorithms and highlight the critical factors influencing these bounds, such as the amounts of training data, the complexity of the hypothesis space, the quality of pre-trained models, and the discrepancy of the reconstruction feature distribution. The numerical experiments show the effectiveness of the proposed algorithms, particularly in their application to activity recognition clustering tasks.

Jing Zhang, Chenping Hou

Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, P. R. China. · College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, Hunan, 410073, China.

Clustering Generalization Bounds

Mar 20, 2026

Distributed Gradient Clustering: Convergence and the Effect of Initialization

We study the effects of center initialization on the performance of a family of distributed gradient-based clustering algorithms introduced in [1], that work over connected networks of users. In the considered scenario, each user contains a local dataset and communicates only with its immediate neighbours, with the aim of finding a global clustering of the joint data. We perform extensive numerical experiments, evaluating the effects of center initialization on the performance of our family of methods, demonstrating that our methods are more resilient to the effects of initialization, compared to centralized gradient clustering [2]. Next, inspired by the

K

-means++ initialization [3], we propose a novel distributed center initialization scheme, which is shown to improve the performance of our methods, compared to the baseline random initialization.

Aleksandar Armacki, Himkant Sharma, Dragana Bajović +3

Carnegie Mellon University, Pittsburgh, Pennsylvania, USA · Indian Institute of Technology Kharagpur, Kharagpur, India · Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia +1

Clustering Distributed Optimization

Mar 20, 2026

A Super Fast K-means for Indexing Vector Embeddings

We present SuperKMeans: a k-means variant designed for clustering collections of high-dimensional vector embeddings. SuperKMeans' clustering is up to 7x faster than FAISS and Scikit-Learn on modern CPUs and up to 4x faster than cuVS on GPUs (Figure 1), while maintaining the quality of the resulting centroids for vector similarity search tasks. SuperKMeans acceleration comes from reducing data-access and compute overhead by reliably and efficiently pruning dimensions that are not needed to assign a vector to a centroid. Furthermore, we present Early Termination by Recall, a novel mechanism that early-terminates k-means when the quality of the centroids for retrieval tasks stops improving across iterations. In practice, this further reduces runtimes without compromising retrieval quality. We open-source our implementation at https://github.com/cwida/SuperKMeans

Leonardo Kuffo, Sven Hepkema, Peter Boncz

CWI, Amsterdam, The Netherlands · Systems Group, ETH Zurich, Zurich, Switzerland

Mar 20, 2026

Explainable cluster analysis: a bagging approach

A major limitation of clustering approaches is their lack of explainability: methods rarely provide insight into which features drive the grouping of similar observations. To address this limitation, we propose an ensemble-based clustering framework that integrates bagging and feature dropout to generate feature importance scores, in analogy with feature importance mechanisms in supervised random forests. By leveraging multiple bootstrap resampling schemes and aggregating the resulting partitions, the method improves stability and robustness of the cluster definition, particularly in small-sample or noisy settings. Feature importance is assessed through an information-theoretic approach: at each step, the mutual information between each feature and the estimated cluster labels is computed and weighted by a measure of clustering validity to emphasize well-formed partitions, before being aggregated into a final score. The method outputs both a consensus partition and a corresponding measure of feature importance, enabling a unified interpretation of clustering structure and variable relevance. Its effectiveness is demonstrated on multiple simulated and real-world datasets.

Federico Maria Quetti, Elena Ballante, Silvia Figini +1

Department of Mathematics, University of Pavia, Pavia, 27100, Italy. · Department of Social and Political Sciences, University of Pavia, Pavia, 27100, Italy. · Department of Economics and Management, University of Pavia, Pavia, 27100, Italy.

Clustering Unsupervised Clustering