Clustering

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Overview

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

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

May 28, 2026

CLUBench: A Clustering Benchmark

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.

Feng Xiao, Dazhi Fu, Chris Ding +1

The Chinese University of Hong Kong (Shenzhen)

Benchmark DesignClusteringUnsupervised ClusteringDeep Clustering
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May 27, 2026

Fitting Unknown Number of Hyperplanes with Manifold Optimization

Fitting an unknown number of hyperplanes to data is a fundamental yet challenging problem in machine learning, characterized by its non-convexity, non-differentiability, and unknown model order. Existing approaches often struggle with local optima or lack geometric consistency. To address these limitations, we propose a novel framework based on Manifold Optimization. We reformulate the problem as an unsupervised learning task on the unit sphere manifold Sdim−1\mathcal{S}^{\textbf{dim}-1}. This formulation effectively handles the non-convex constraints and linearizes the distance measurement, rendering the gradient descent tractable. We propose a Two-Stage Manifold Optimization algorithm. In Phase I, we employ a Riemannian Expectation-Maximization process with a heavy-tailed kernel to robustly estimate posterior probabilities, effectively resolving the ambiguities of point distribution between intersecting hyperplanes. In Phase II, upon convergence of the soft estimates, the probabilistic weights degenerate into hard matching, generating a precise local optimum that strictly satisfies the geometric definition. Furthermore, we introduce a projected density estimation strategy for initialization to facilitate global convergence by significantly reducing the feature description space and search complexity. Extensive experiments demonstrate that our method outperforms state-of-the-art baselines in both geometric accuracy and robustness.

Zhiqin Cheng, Yu Zhan, Mingjin Zhang +2

Department of Computing, The Hong Kong Polytechnic University, Kowloon, Hong Kong · Department of Electronic and Electrical Engineering, Southern University of Science and Technology, ShenZhen, China · Research Institute of Multiple Agents and Embodied Intelligence, Pengcheng Laboratory, ShenZhen, China +1

Clustering
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May 27, 2026

SmartIterator: Visual Analytics Workflows for Supervising Unsupervised Data Grouping

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 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 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 ∼1 500{\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.

Gennady Andrienko, Natalia Andrienko

Fraunhofer Institute IAIS, Sankt Augustin, Germany, the Lamarr Institute for Machine Learning and Artificial Intelligence, Sankt Augustin, Germany, and City St George’s, University of London, UK.

Scientific VisualizationData VisualizationUnsupervised LearningClusteringUnsupervised ClusteringVisual Analytics
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May 23, 2026

Affinity Graph Connectivity in Convex Clustering

We generalize finite-sample bounds for convex clustering to the setting where affinity weights appearing in the objective correspond to a general connected graph. These bounds and their analysis lead to a better understanding of clustering behavior under various implied connectivity structures behind the data and to new rates of convergence for centroid recovery. The new theoretical framework is based on random walks, which allow application of concentration inequalities related to random graph models, and formalizes the relationship between the clustering performance and the connectivity of the graph structures. Through the form of the bound and empirical results, we argue proper tuning of hyperparameters to convex clustering problems should also include tuning of input affinity weights.

Sam Rosen, Jason Xu

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

Clustering
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May 23, 2026

Clustering based on Stochastic Dominance with application for risk averters and risk seekers

Stochastic Dominance (SD) theory provides a rigorous framework for selecting superior assets tailored to the asset allocation needs of investors with varying risk preferences (i.e., risk-averse, risk-seeking, and risk-neutral). However, traditional stock clustering methods typically rely on geometric metrics such as Euclidean distance, which often fail to effectively capture the intrinsic risk dominance relationships among assets. To address this limitation, this paper proposes an innovative clustering analysis framework based on SD test statistics. Methodologically, this study deeply integrates SD theory with machine learning algorithms. Transcending the limitations of traditional reliance on geometric distance, we innovatively utilize test statistics from first-, second-, and third-order SD to construct a "Stochastic Dominance Coefficient Matrix." Building upon this matrix, we modify the classic K-means and Hierarchical Clustering algorithms. Specifically, we derive 12 distinct algorithm variants tailored to different orders of SD relationships. Simultaneously, we construct the SD-SC coefficient and the SD-DBI index as specialized validity indices to evaluate the clustering performance. Empirically, we analyze constituent stock data from a representative developed market (the US NASDAQ Index) and an emerging market (China's CSI 100 Index). The results verify the effectiveness and robustness of the proposed method. Furthermore, we apply the clustering results to the modification of the Single Index Model and the construction of Global Minimum Variance Portfolios (GMVP). The findings demonstrate that the proposed method effectively facilitates customized asset allocation for investors, holding significant theoretical value and practical implications.

Hua Li, Xue Jia, Yilin Kang +1

School of Science, Changchun University, Changchun, China. · School of Mathematics and Science, Northeast Normal University, Changchun, China.

Quantitative FinanceClusteringUnsupervised Clustering
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May 23, 2026

How Much Structure Do LLMs Need? Evaluating LLMs for Bibliometric Cluster Description

Large language models (LLMs) can support scientific literature synthesis, but remain prone to hallucinated references, uneven coverage, and weakly grounded thematic organization. We evaluate whether bibliometric structure improves LLM-assisted synthesis by comparing six pipelines for generating cluster descriptions under different levels of evidence and structure. Using 100 published bibliometric analyses, we reconstruct Scopus corpora, extract human-written cluster descriptions, and assess outputs by human alignment, semantic coverage, clustering quality, graph quality, and reference grounding. Results show that LLMs produce descriptions semantically close to human-written ones, but are unreliable when asked to infer bibliometric structure from scratch. Performance improves when bibliometric algorithms define the clusters and the LLM interprets them. Overall, LLM-assisted bibliometric synthesis is most promising as a hybrid workflow in which algorithms provide auditable structure and LLMs generate readable descriptions.

Abraham Camelo-Guerrero, Jairo Diaz-Rodriguez

School of Information Technology York University Toronto, Ontario M3J 1P3 · Department of Mathematics and Statistics York University Toronto, Ontario M3J 1P3

LLM EvaluationClusteringAI-Assisted Scientific ResearchBibliometric Analysis
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May 22, 2026

Benchmarking Patent Embeddings: A Multi-Task Evaluation of 22 Models Across Retrieval, Classification, and Clustering

Two questions regarding practitioners' use of patent embeddings arise: (i) Does one fine-tuning recipe suffice for all downstream applications? (ii) Is fine-tuning on one patent landscape sufficient for downstream application on other landscapes? By evaluating 22 pre-trained embedding models (ranging from 22M to 12B parameters) on three tasks -- information retrieval, classification, and clustering -- on 113,148 WIPO patents for assistive technology (46,069 citation queries) and on an external DAPFAM dataset, we find that two results cast doubt on the prevailing wisdom. (i) The optimal fine-tuning recipe depends on the downstream task: cross-sectional alignment (recipe R3) provides the largest improvements to retrieval performance (+7.1% nDCG@10), whereas a combined signal recipe (recipe R4) is better suited to classification (+7.1 F1) and clustering (+10.9 V-measure); a matched data control confirms that differences in training dataset size are not a contributing factor. (ii) Single-landscape fine-tuning hampers cross-landscape information retrieval: fine-tuning on one landscape significantly degrades cross-domain retrieval for 5 of 8 model-recipe combinations on the DAPFAM corpus, with the stronger zero-shot models suffering most. While within-family scaling is consistent (Qwen3 0.6B->4B->8B; Llama-Nemotron 1B->8B), cross-family scaling is erratic; the 12B KaLM-Gemma3 is ranked 8th on TAC retrieval performance, following prefix modification. Title+Abstract+Claims is the ubiquitous best text view, and all models suffer from a 55-65% gap between IN and OUT-of-domain performance which cannot be mitigated by hybrid BM25-dense fusion. Code and evaluation framework are publicly available.

Amirhossein Yousefiramandi, Ciaran Cooney

Clarivate, Intellectual Property Barcelona, Spain 08025

Legal IRClusteringText Embedding EvaluationText ClassificationInformation RetrievalIR Evaluation
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May 22, 2026

Detecting Metastable Basins in High Dimensions via Marginal Trajectory Distribution Discrimination

We study the problem of identifying dynamically distinct basins of attraction in high dimensional time-homogeneous Markov processes using only trajectory sampling. This problem is fundamental in the analysis of metastable dynamical systems, where the process rapidly mixes within basins while transitions between basins occur rarely on the timescale of interest, or even when the state space is reducible. Existing approaches typically rely on spatial discretization or spectral analysis of estimated transition operators, which can become unreliable in high dimensional settings or when the underlying basin geometry is highly nonlinear. We propose a discriminative approach to basin identification based on marginal trajectory distribution comparison. We prove a simple risk separation result: if two initial states belong to the same basin, the Bayes-optimal classifier distinguishing their marginal trajectory distributions achieves risk close to 1/2, whereas if they lie in distinct basins, the optimal risk is close to zero. This observation reduces basin detection to a two-sample discrimination problem between marginal trajectory distributions. Motivated by this principle, we develop a neural algorithm that receives a set of candidate basin representatives and iteratively merges them by estimating classification risk with a neural network that approximates the Bayes classifier. We evaluate the method on various metastable systems. These include synthetic systems constructed by embedding low-dimensional dynamics into high dimensional noisy ambient spaces. In these settings, standard spectral and clustering-based methods often fail, while our approach accurately recovers the underlying basin structure. These results display a shortcoming of existing methods and highlight trajectory discrimination as an effective tool for identifying dynamical basins in high dimensional stochastic systems.

Taj Jones-McCormick

Dynamical SystemsTwo-Sample TestingClustering
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May 21, 2026

EnCAgg: Enhanced Clustering Aggregation for Robust Federated Learning against Dynamic Model Poisoning

Federated learning faces increasing threats from model poisoning attacks, which harms its application to improve privacy. Existing defense methods typically rely on fixed thresholds or perform clustering with a fixed number of clusters to distinguish malicious gradients from benign ones. However, these methods are difficult to adapt to dynamic poisoning strategies of malicious clients, and often result in the loss of benign gradients due to the heterogeneity of clients' local datasets. To address these problems, we propose a novel robust aggregation method that leverages a small number of known benign clients as references, enabling accurate identification and filtering of malicious gradients while retaining as many benign gradients as possible, even when the number of malicious clients is unknown and variable. First, we introduce a density-based low-dimensional gradient clustering method, which projects gradients onto the two most divergent dimensions and applies density-based clustering to identify malicious gradients while retaining clustered benign gradients and potentially benign outliers. Second, we design an enhancing clustering low-dimensional gradient generator model, which learns to generate pseudo-gradients aligned with the boundary of the benign cluster. These pseudo-gradients act as bridges to connect sparse benign gradient outliers. Third, we introduce low-dimensional gradient re-clustering that clusters the generated pseudo-gradients together with real gradients to recover benign gradients misclassified as noise points, enabling more benign gradients to participate in aggregation. Extensive experiments on the MNIST, CIFAR-10, and MIND datasets demonstrate that our method exhibits superior fidelity and robustness under dynamic poisoning scenarios.

Tianyun Zhang, Zhen Yang, Haozhao Wang +2

School of Cyberspace Security, Beijing University of Posts and Telecommunications, Beijing 100876, China · School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, China · Department of Electronic Engineering, Tsinghua University, Beijing 100084, China

Federated Learning AggregationByzantine-Robust Federated LearningAdversarial AttacksClusteringDensity-Based ClusteringFederated Learning
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May 21, 2026

Minimum Description Length based Granular-Ball Tree Regularization for Spectral Clustering

Spectral clustering largely depends on the affinity graph, yet constructing a graph that preserves reliable local connectivity while adapting to heterogeneous data structures remains challenging. Existing granular-ball-based spectral clustering methods usually reduce graph complexity by using coarse-grained representatives. However, the learned local regions are often treated as graph nodes or anchors, and their structural information is not sufficiently used to regularize the original sample-level graph. To address this issue, this paper proposes a Minimum Description Length based Granular-Ball Tree-Regularized Spectral Clustering method, termed MDL-GBTRSC. The proposed method constructs a granular-ball tree through local MDL model selection, with reciprocal neighborhood continuity used to discourage splits that break reliable local connections. The stable leaf balls obtained from the tree provide coding-scale information for regularizing the sample-level affinity graph. In addition, a shared-neighbor bridge code is introduced to adjust weak local bridge relations without requiring an additional user-specified threshold. In this way, MDL-GBTRSC connects interpretable local representation learning with affinity graph construction in a unified spectral clustering framework. Experiments on real and synthetic datasets show that MDL-GBTRSC achieves the best average ARI and NMI under the adopted fixed-configuration protocol compared with classical spectral clustering baselines and representative granular-ball, micro-cluster, and anchor-based methods.

Zeqiang Xian, Caihui Liu, Yong Zhang +1

Department of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, Jiangxi, China · Key Laboratory of Data Science and Artificial Intelligence of Jiangxi Education Institutes, Gannan Normal University, Ganzhou 341000, Jiangxi, China

Graph Structure LearningClusteringSpectral Clustering
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May 20, 2026

Unsupervised clustering and classification of upper limb EMG signals during functional movements: a data-driven

This study presents a comprehensive approach for the clustering and classification of upper-limb surface electromyography (sEMG) signals during functional reach and grasp movements. The methodology was applied to the NINAPRO DB4 dataset, which provides multichannel EMG recordings of 52 gestures. A four-stage pipeline was designed, including signal preprocessing, fea-ture extraction, gesture selection via hierarchical clustering, and comparative model evaluation. Preprocessing involved a fourth-order low-pass filter (0.6 Hz) and Hilbert envelope transformation, effectively reducing noise and enhancing signal clarity. Feature extraction yielded 26 temporal and frequency-domain met-rics, which were later refined using visual analysis, mutual information, principal component analysis, and decision tree importance scores. A final subset of five key features was selected for classification tasks. Gesture selection was per-formed through hierarchical clustering using Mahalanobis distance, resulting in six representative movements that balanced biomechanical diversity and compu-tational efficiency. A 200 ms window was identified as optimal for temporal seg-mentation based on stability and physiological plausibility. Classifier models were evaluated in two stages. Automated comparison using PyCaret identified Extra Trees (ET) and Artificial Neural Networks (ANN) as top performers. Sub-sequent independent training confirmed their stability and generalization capac-ity, with ANN showing progressive learning and ET maintaining robust, con-sistent results. The findings support the implementation of adaptive, low-latency control strategies for myoelectric prostheses and provide a scalable pipeline for future real-time applications.

L. F. Salazar Álvarez, D. Escobar-Saltarén, M. B. Salazar Sánchez +1

In2Lab, Engineer Faculty, Universidad de Antioquia. Medellín, Calle 70 No. 52-21, A.A. 1226 · School of Engineering and Sciencies, Tecnológico de Monterrey. Guadalajara, México

EMG-Based Gesture RecognitionClusteringHierarchical ClusteringGesture Recognition
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May 19, 2026

A Unified Framework for Structure-Aware Clustering and Heterogeneous Causal Graph Learning

In complex multivariate systems, interactions among variables are defined by dependency structures, often encoded as directed acyclic graphs (DAGs\text{DAGs}). However, dependency structures can vary across subjects, and ignoring this structural heterogeneity introduces bias and obscures subpopulation-specific dependencies. To address this, we propose Directed Acyclic Graph-based Dependency Clustering via Alternating Direction Method of Multipliers (DAG-DC-ADMM), a unified framework built upon Structural Equation Modeling (SEM) that jointly learns cluster assignments and cluster-specific dependency structures. We encode acyclicity via a smooth constraint and integrate a groupwise truncated Lasso fusion penalty (gTLP) to cluster subjects based on their structural similarity. This yields a nonconvex optimization problem that incorporates sparsity, acyclicity, and structural consensus constraints. We address the nonconvexity by using the augmented Lagrangian method and solve it with an adapted version of the Alternating Direction Method of Multipliers (ADMM) for difference-of-convex programs. For certain graph structures, such as upper triangular adjacency matrices, our algorithm is guaranteed to converge to a Karush-Kuhn-Tucker (KKT) point. Experiments demonstrate that our method recovers cluster-specific causal dependency structures with a high true positive rate and a low false discovery rate. This capability enables the robust discovery of heterogeneous dependencies across subjects where the subpopulation label is unknown.

Honglin Du, Muxuan Liang, Xiang Zhong

Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL 32611, USA · Department of Biostatistics, MD Anderson Cancer Center, Houston, TX 77030, USA

Structural Causal ModelsClusteringCausal DiscoveryCausal Structure LearningAlternating Direction Method of Multipliers
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May 18, 2026

GUT-IS: A Data-Driven Approach to Integrating Constructs and Their Relations in Information Systems

Structural equation modeling is widely used in IS research. However, inconsistent construct definitions impede the cumulative development of knowledge. In this work, we present an approach that aims at the integration of structural equation models into a unified model: We use a combination of task-adapted text embeddings and clustering to produce a candidate set of construct groupings. Subsequently, we select the optimal solution using a loss function that explicitly trades off semantic purity and parsimony in the number of clusters. By making this trade-off explicit, our approach allows to analyze how construct groupings and their relations change as one shifts the priority from purity to parsimony. Empirically, we evaluate and explore the proposed methodology on two datasets from the IS domain.

Maximilian Reinhardt, Jonas Scharfenberger, Burkhardt Funk

Institute of Information Systems Leuphana University Lüneburg, Germany

Latent Variable ModelsClusteringText Clustering
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May 18, 2026

When Fireflies Cluster; Enhancing Automatic Clustering via Centroid-Guided Firefly Optimization

This work presents a novel variant of the Firefly Algorithm (FA) for data clustering, addressing limitations of traditional methods like K-Means that struggle with non-uniform cluster shapes, densities, and the need for pre-defining the number of clusters. The proposed algorithm introduces a centroid movement strategy and a multi-objective fitness function that balances compactness, separation, and a novel TSP-based navigation penalty. It automatically estimates the optimal number of clusters and dynamically adjusts cluster boundaries. Application to robotic sensor networks highlights its practical value, with experiments showing improved clustering quality and reduced intra-cluster path distances compared to K-Means. These results confirm the algorithm's robustness in complex spatial clustering tasks, with potential for future extensions to higher-dimensional and adaptive scenarios.

MKA Ariyaratne, Azwirman Gusrialdi, Yury Nikulin +1

Department of Computer Science, Faculty of Applied Sciences, University of Sri Jayewardenepura, Sri Lanka · Faculty of Engineering and Natural Sciences,Tampere University, Tampere, Pirkanmaa, Finland · Department of Mathematics and Statistics, University of Turku, Finland

Multi-Objective Evolutionary OptimizationMetaheuristic OptimizationClusteringUnsupervised Clustering
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May 17, 2026

TextClusterLab: An Integrated Framework for Reliable Text Clustering Studies

In recent years, text clustering has become a critical technique for applications including intent discovery, topic mining, and recommendation systems. However, evaluating text clustering algorithms remains challenging since many real-world textual datasets are not suitable for clustering assessment due to ambiguous semantic boundaries, the high dimensionality of embeddings, and inconsistent cluster structure. Current clustering dataset generators are designed for numerical data, providing limited support for text-specific benchmarking. This paper introduces TextClusterLab, a comprehensive framework for text clustering research. TextClusterLab offers a Large Language Model (LLM)-driven text clustering dataset generator to produce synthetic text datasets for evaluating clustering algorithms. This generator supports setting various clustering attributes, such as class imbalance, intra-cluster compactness, and inter-cluster diversity. These generated datasets can serve as practical benchmarks for testing the robustness and versatility of text clustering algorithms in diverse scenarios. Moreover, we introduce a benchmark to verify whether a text dataset is suitable for clustering evaluation. Therefore, TextClusterLab provides an integrated framework for reproducible and comprehensive text-specific clustering research. Our TextClusterLab is publicly available at https://github.com/research-paper-code/TextClusterLab, and some synthetic example datasets with various attributes are publicly available at https://huggingface.co/datasets/DW-irlab/TextClusterLab.

Daoming Wan, Yizheng Huang, Jimmy X. Huang

Information Retrieval and Knowledge Management Research Lab, York University Toronto, Ontario, Canada

ClusteringSynthetic Data GenerationSynthetic Benchmark GenerationText ClusteringSynthetic Data Evaluation
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May 16, 2026

An Analytical Multiple Criteria Framework for Temporal and Dynamic Business-to-Business Customer Segmentation in Manufacturing

In sales and marketing, customer segmentation is an important tool for formulating strategies for customer treatment and supply chain management. Most segmentation implementations rely on limited criteria, such as recency, frequency, and monetary (RFM) modeling, which often fail to capture complex business interactions. In this work, we design and evaluate a dynamic multi-criteria decision-making (MCDM) method in a business-to-business (B2B) manufacturing context by 1) extending RFM to dimensions of stability and growth, 2) integrating an adaptive and analytical hierarchical process to match business objectives, and 3) evaluating multivariate time-series clustering models. We then measure customer stability, tracking between-segment transitions, and volatility over time, and apply a graph-based consensus model to further strengthen the analysis. We test the efficacy of the proposed method using a real-world manufacturing company dataset to segment more than 3,000 B2B customers, showing strong robustness to temporal shifts. The implementation enables domain experts with preferential analytics to devise their strategies, providing effective decision support for B2B customer segmentation.

Muhammad Raees, Konstantinos Papangelis, Vassilis Javed Khan

Rochester Institute of Technology Rochester NY USA · Independent Researcher

ClusteringMulti-Criteria Decision AnalysisTime Series Clustering
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May 16, 2026

Capturing LLM Capabilities via Evidence-Calibrated Query Clustering

Query clustering organizes queries into groups that reflect shared latent capability demands, enabling capability-aware LLM evaluation. Existing clustering methods, which primarily rely on semantic taxonomies or embeddings, often fail to capture such latent capability requirements due to a misalignment between surface-level semantics and actual model performance. We propose ECC, an algorithm that calibrates prior semantic embeddings using limited posterior model comparisons to bridge the gap between surface-level semantics and latent capability requirements. ECC characterizes each cluster through a capability profile parameterized by a Bradley-Terry model and uses trainable mixture weights to accommodate queries with mixed capability demands, jointly learning a flexible, capability-aware clustering structure that supports query-specific inference of LLM capabilities. Extensive quantitative and qualitative evaluations demonstrate that ECC significantly improves LLM capability ranking quality, outperforming human-labeled and embedding-based baselines by an average of 17.64 and 18.02 percentage points, respectively, and proves effective in downstream tasks such as query routing.

Fangzhou Wu, Sandeep Silwal, Qiuyi Zhang

University of Wisconsin–Madison · 2Elorian AI

LLM EvaluationClustering
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May 14, 2026

K-Models: a Flexible and Interpretable Method for Ordinal Clustering with Application to Antigen-Antibody Interaction Profiles

Existing clustering methods for functional data often prioritize partitioning accuracy over interpretability, making it challenging to extract meaningful insights when the data-generating process follows a specific underlying structure and an ordinal relationship among clusters is suspected. This work introduces K-Models, a novel framework that integrates ordinal constraints and estimates key underlying elements of the random process generating the observed functional profiles, improving both interpretability and structure identification. The proposed method is evaluated through simulations and real-world applications. In particular, it is tested on Region of Interest (ROI) curves, which represent reaction profiles from a reflectometric sensor monitoring biomolecular interactions, such as antigen-antibody binding. These curves represent changes in reflected light intensity over time at multiple measurement spots with immobilized antigens during analyte exposure, capturing the binding dynamics of the system. The goal is to identify intrinsic signal patterns solely from the observed dynamics, making this dataset an ideal benchmark for assessing the added interpretability of the proposed approach. By incorporating structural assumptions into the clustering process, K-Models enhances interpretability while maintaining performance comparable to state-of-the-art techniques, providing a valuable tool for analyzing functional data with an underlying ordinal structure.

Giulia Patanè, Alessandra Menafoglio, Alexander Krauth +4

MOX, Department of Mathematics, Politecnico di Milano, Piazza Leonardo da Vinci 32, Milan, 20133, Italy. · Institute of Physical and Theoretical Chemistry (IPTC), Eberhard Karls Universität Tübingen, Auf der Morgenstelle 18, Tübingen, 72076, Germany. · Department of Mechanical Engineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, Milan, 20133, Italy.

Clustering
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May 14, 2026

ToMAToMP: Robust and Multi-Parameter Topological Clustering

Topological clustering, and its main algorithm ToMATo, is a clustering method from Topological Data Analysis (TDA) which has been applied successfully in several applications during the last few years. This is due to its high versatility, as clusters are detected from the persistent components in the sublevel sets of any user-defined function (gene expression, pixel values, etc), and efficiency, as topological clustering enjoys robustness guarantees. However, ToMATo is also limited in several ways. First, a graph on the data points needs to be provided as a hyper-parameter of the method (whose fine-tuning is left to the user). Second, ToMATo is known to be very sensitive to outlier values in the function range. Finally, and most importantly, ToMATo can only handle one function at a time, whereas it is critical to use several functions in various applications. In this article, we introduce ToMAToMP: the first topological clustering method able to handle several functions at the same time with theoretical guarantees. More specifically, we leverage a recent tool from multi-parameter persistent homology, called MMA decomposition, to design our clustering algorithm, and prove that it enjoys robustness properties. As corollaries, we show that it can be used to make ToMATo independent of graph tuning, and robust to outliers. Finally, we provide a set of numerical experiments showcasing the efficiency and quality of the clusterings produced by ToMAToMP, by showing strong improvement over non-topological and topological baselines for various datasets.

Ludo Andrianirina, Mathieu Carrière

DataShape, Centre Inria d’Université Côte d’Azur, Sophia-Antipolis, France

ClusteringPersistent HomologyTopological Data Analysis
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May 13, 2026

Fast and effective algorithms for fair clustering at scale

Clustering is an unsupervised machine learning task that consists of identifying groups of similar objects. It has numerous applications and is increasingly used in fairness-sensitive domains where objects represent individuals, such as customers, employees, or students. We address a fair clustering problem in which objects belong to protected groups. The problem consists of partitioning the objects into a predefined number of clusters while attaining a user-defined target level of fairness, meaning that each protected group is sufficiently represented in each cluster. The objective is to minimize the clustering cost, defined as the sum of squared Euclidean distances between the objects and the centers of their clusters. Since clustering cost and fairness are generally in conflict, managing the trade-off between them is essential in practical applications. Existing methods provide limited control over this trade-off and either fail to scale to large datasets or, when they scale, produce low-quality solutions. We propose a general framework for fair clustering that provides precise control over the cost-fairness trade-off and introduce three heuristics based on it. The first heuristic focuses on solution quality and the flexibility to incorporate additional constraints, the second improves scalability while retaining high solution quality, and the third is designed for maximum scalability, producing solutions for instances with millions of objects in seconds. The proposed heuristics outperform existing approaches in comprehensive numerical experiments on benchmark datasets. The source code of our heuristics and instructions for reproducing the experiments are publicly available on GitHub.

Claudio Mantuano, Manuel Kammermann, Philipp Baumann

Department of Business Administration, University of Bern, Engehaldenstrasse 4, 3012 Bern, Switzerland

ClusteringAlgorithmic FairnessGroup Fairness
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May 13, 2026

Amortized Neural Clustering of Time Series based on Statistical Features

This paper introduces an algorithm-agnostic approach to feature-based time series clustering via amortized neural inference. By training neural networks to approximate the optimal partitioning rule from simulated data, the proposed framework reduces reliance on conventional clustering methods, such as KK-means, KK-medoids, or hierarchical clustering, and their associated objective functions and heuristics. Leveraging statistical features, such as autocorrelations and quantile autocorrelations, the approach learns a data-driven affinity structure from which clustering partitions can be recovered, without requiring explicit prior specification of cluster shapes or structures. In addition, one version of the method can automatically determine the number of clusters, avoiding ad-hoc selection procedures. Comprehensive empirical studies show that the proposed framework achieves competitive or superior clustering accuracy relative to traditional methods, even in challenging scenarios where competing techniques are provided with the true number of clusters. An application to financial time series of stock returns illustrates its practical utility. By reducing the need for algorithm selection and calibration, the proposed framework opens new possibilities for automated, adaptive, and data-driven clustering of temporal data across scientific and industrial domains.

Ángel López-Oriona, Ying Sun

CEMSE Division, Statistics Program, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia. · Statistics Program, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia

Cluster Number EstimationAmortized InferenceClusteringUnsupervised ClusteringTime Series Clustering
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May 13, 2026

Reducing Bias and Variance: Generative Semantic Guidance and Bi-Layer Ensemble for Image Clustering

Image clustering aims to partition unlabeled image datasets into distinct groups. A core aspect of this task is constructing and leveraging prior knowledge to guide the clustering process. Recent approaches introduce semantic descriptions as prior information, most of which typically relying on matching-based techniques with predefined vocabularies. However, the limited matching space restricts their adaptability to downstream clustering tasks. Moreover, these methods primarily focus on reducing bias to improve performance, frequently overlooking the importance of variance reduction. To address these limitations, we propose GSEC (Image Clustering based on Generative Semantic Guidance and Bi-Layer Ensemble), a framework designed to reduce bias through generative semantic guidance and mitigate variance via ensemble learning. Our method employs Multimodal Large Language Models to generate semantic descriptions and derive image embeddings via weighted averaging. Additionally, a bi-layer ensemble strategy integrates cross-modal information through BatchEnsemble in the inner layer and aligns outputs via an alignment mechanism in the outer layer. Comparative experiments demonstrate that GSEC outperforms 18 state-of-the-art methods across six benchmark datasets, while further analysis confirms its effectiveness in simultaneously reducing both bias and variance. The code is available at https://github.com/2017LI/GSEC.git.

Feijiang Li, Zhenxiong Li, Jieting Wang +3

Institute of Big Data Science and Industry, Shanxi University · Key Laboratory of Evolutionary Science Intelligence of Shanxi Province · School of Artificial Intelligence, Shanxi University

Ensemble LearningClusteringImage ClusteringVariance Reduction
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May 12, 2026

H2G: Hierarchy-Aware Hyperbolic Grouping for 3D Scenes

Hierarchical 3D grouping aims to recover scene groups across multiple granularities, from fine object parts to complete objects, without relying on semantic labels or a fixed vocabulary. The main challenge is to transform 2D foundation-model cues into coherent hierarchy supervision and embed that hierarchy in a 3D representation. We propose H2G, a hyperbolic affinity field for hierarchical 3D grouping. Our method derives semantically organized tree supervision by interpreting foundation-model affinities through Dasgupta's objective for similarity-based hierarchical clustering. This supervision is distilled into a single Lorentz hyperbolic feature field, whose geometry is well suited for tree-like branching structures. A hierarchy-aware objective aligns the field with fine-level assignments, coarse object structure, compact feature clusters, and LCA (Lowest Common Ancestor) ordering. This formulation represents multiple grouping levels in one feature space, enabling semantic hierarchical grouping grounded in 2D foundation-model knowledge.

ByungHa Ko, Youngmin Lee, Dong Hwan Kim

Department of Computer Science and Engineering, Korea University · Intelligence and Interaction Research Center, Korea Institute of Science and Technology

ClusteringHierarchical Representation Learning3D Representation LearningHyperbolic Representation Learning
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May 11, 2026

Beyond Majority Voting: Agreement-Based Clustering to Model Annotator Perspectives in Subjective NLP Tasks

Disagreement in annotation is a common phenomenon in the development of NLP datasets and serves as a valuable source of insight. While majority voting remains the dominant strategy for aggregating labels, recent work has explored modeling individual annotators to preserve their perspectives. However, modeling each annotator is resource-intensive and remains underexplored across various NLP tasks. We propose an agreement-based clustering technique to model the disagreement between the annotators. We conduct comprehensive experiments in 40 datasets in 18 typologically diverse languages, covering three subjective NLP tasks: sentiment analysis, emotion classification, and hate speech detection. We evaluate four aggregation approaches: majority vote, ensemble, multi-label, and multitask. The results demonstrate that agreement-based clustering can leverage the full spectrum of annotator perspectives and significantly enhance classification performance in subjective NLP tasks compared to majority voting and individual annotator modeling. Regarding the aggregation approach, the multi-label and multitask approaches are better for modeling clustered annotators than an ensemble and model majority vote.

Tadesse Destaw Belay, Ibrahim Said Ahmad, Idris Abdulmumin +6

1Instituto Politécnico Nacional · University of Wisconsin–Stevens Point · University of Pretoria +3

Annotator DisagreementClustering
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May 9, 2026

MDL-GBG: A Non-parametric and Interpretable Granular-Ball Generation Method for Clustering

Existing granular-ball generation methods are still mainly driven by handcrafted quality measures and heuristic splitting or stopping criteria, which may weaken the transparency of local generation decisions in clustering. To address this issue, this paper proposes Minimum Description Length based Granular-Ball Generation (MDL-GBG), a non-parametric and interpretable granular-ball generation method for clustering. MDL-GBG reformulates granular-ball generation as a local model selection problem under the Minimum Description Length principle. For each granular ball, three candidate explanations are compared, namely a single-ball model, a two-ball model, and a core-ball-plus-residual model, and the model with the shortest description length is selected. In this way, ball retention, splitting, and residual peeling are unified within a common coding-theoretic framework. A residual reassignment mechanism is further introduced to re-evaluate peeled-off boundary samples after stable granular-balls are formed. Experiments on 20 UCI datasets show that the stable granular-balls generated by MDL-GBG provide an effective upstream representation for clustering. In particular, MDL-GBG+AC achieves the best average ranks in ARI, ACC, and NMI among the compared methods. These results indicate that MDL-GBG offers a principled and interpretable alternative to heuristic granular-ball generation strategies.

Zeqiang Xian, Caihui Liu, Yong Zhang +3

Department of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, Jiangxi, China · Key Laboratory of Data Science and Artificial Intelligence of Jiangxi Education Institutes, Gannan Normal University, Ganzhou 341000, Jiangxi, China · Department of Computer Science and Technology, Tongji University, 201804 Shanghai, China +1

ClusteringUnsupervised Clustering
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May 9, 2026

PHIDA: Persistence-Guided Node-to-Cluster Mapping for Online Clustering

Online clustering methods that adaptively create and update nodes as data arrive often make node learning explicit, whereas the mapping from the learned node state to output clusters often remains implicit or simplified. Implicit mappings make output clusters sensitive to weak graph bridges or local relations based on distance in the graph over learned nodes, leaving no explicit constraint on which node groups remain intact during mapping. This paper addresses this gap by proposing PHIDA, a persistence-guided node-to-cluster mapping method for online clustering with learned nodes. PHIDA implements this mapping within Adaptive Resonance Theory (ART)-based online clustering by combining Inverse-Distance ART (IDA) node learning with node-to-cluster mapping constrained by Persistent Homology (PH). Experiments on 24 benchmark datasets show that PHIDA achieves the best average ranks in stationary comparisons that include the recent stationary-only clustering methods, while also improving aggregate performance in the nonstationary setting over the evaluated online methods that adaptively create and update nodes. Ablations and comparisons with conventional node-to-cluster mappings indicate that the observed gains are associated with PH-constrained mapping that preserves raw PH components, together with the use of the PH component view during node learning. Source code is available at https://github.com/Masuyama-lab/PHIDA

Naoki Masuyama, Yusuke Nojima, Stefan Wermter +3

Graduate School of Informatics, Osaka Metropolitan University · Knowledge Technology Research Group, Department of Informatics, University of Hamburg · Graduate School of Environmental, Life, Natural Science and Technology, Okayama University +2

ClusteringUnsupervised ClusteringAdaptive Learning
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May 8, 2026

Training-Induced Escape from Token Clustering in a Mean-Field Formulation of Transformers

Transformers perform inference by iteratively transforming token representations across layers. This layerwise computation has been studied empirically, and recent mean-field theories of Transformer dynamics explain how attention can drive token distributions toward clustering. However, existing analyses treat model parameters as prescribed, leaving open how training reshapes this clustering picture. We study this question in a noisy mean-field Transformer in which only a parameter-linear FFN is trained under L2L^2 regularization. We identify a training-induced phase of the inference dynamics across layers: after clustering in the early layers, the token distribution can leave the clustered regime near the final layers. A single gradient-descent update already produces this escape, and minimizers of the training objective satisfy an exponential turnpike bound under which clustering persists through the interior layers. Our analysis is based on an entropy-regularized interaction energy that captures the clustering bias of attention, for which we establish a double-well landscape and a local Polyak-Łojasiewicz inequality. More broadly, our results point toward a training-aware mean-field theory in which training and inference dynamics of Transformers are treated together.

Noboru Isobe, Daisuke Inoue, Masaaki Imaizumi

RIKEN Center for Advanced Intelligence Project · Imperial College London · The University of Tokyo +1

TransformerTransformer Training DynamicsClusteringTransformer AttentionMean-Field TheoryNeural Network Training Dynamics
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May 8, 2026

A Flexible Adaptive Stable Clustering Algorithm for Archive-Scale Online Mass Spectrometry

Modern online mass spectrometry generates multi-terabyte data streams critical for understanding Earth's environmental systems. However, extracting actionable chemical insights from these repositories is impeded by a computational bottleneck: existing clustering methods force a compromise among scalability, metric flexibility, and algorithmic stability. Here, we introduce Flexible Adaptive Stable Clustering (FASC), a dynamical systems framework that resolves these constraints by architecturally decoupling the similarity kernel from rigorous optimization logic. Unlike legacy heuristics that suffer from stochastic drift and algorithmic blending, FASC employs a Density-Augmented Similarity Selection rule and geometric constraints to guarantee deterministic, order-independent convergence. After validating FASC on canonical machine-learning ground truths (achieving >99.5% cluster purity and 0.99 Adjusted Rand Index), we deployed the framework on 25 million mass spectra of atmospheric aerosols. Demonstrating strictly linear empirical runtime scaling (O(N)), FASC autonomously mapped atmospheric aging pathways of secondary inorganic aerosols while isolating ultra-rare industrial tracers (<0.2% abundance), providing a scalable infrastructure for mining environmental big data.

Shao Shi, Xin Yang, Huiran Feng +8

Shenzhen Key Laboratory of Precision Measurement and Early Warning Technology for Urban Environmental Health Risks, School of Environmental Science and Engineering, Southern University of Science and Technology, 1088 Xueyuan Avenue, Shenzhen, 518055, Guangdong, China. · Guangdong Provincial Observation and Research Station for Coastal Atmosphere and Climate of the Greater Bay Area, Southern University of Science and Technology, 1088 Xueyuan Avenue, Shenzhen, 518055, Guangdong, China.

Algorithmic StabilityClusteringUnsupervised ClusteringMass Spectrometry
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May 8, 2026

Simple KNN-Based Outlier Detection Achieves Robust Clustering

Being robust to the presence of outliers is crucial for applying clustering algorithms in practice. In the \textit{robust k-Means} problem (i.e., kk-Means with outliers), the goal is to remove zz outliers and minimize the kk-Means cost on the remaining points. Despite the close connection between robust kk-Means and outlier detection, both theoretical and empirical understanding of the effectiveness of classic outlier detection heuristics\textit{classic outlier detection heuristics} for robust kk-Means remains limited. In this paper, we prove that under a practical assumption on the optimal cluster sizes, simply removing points with large KK-Nearest-Neighbor distances achieves performance comparable to prior work in terms of approximation guarantees: it yields a constant-factor reduction from robust kk-Means to standard kk-Means, without introducing additional centers or discarding extra outliers, as is commonly required by existing approaches. Empirically, experiments on real-world datasets show that our method outperforms or matches several more sophisticated algorithms in terms of clustering cost and runtime. These results demonstrate that simple KNN-based heuristics can be surprisingly effective for robust clustering, highlighting new opportunities to bridge techniques from outlier detection and clustering.

Tianle Jiang, Yufa Zhou

Duke University

Clustering
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May 8, 2026

Classification Fields: Arbitrarily Fine Recursive Hierarchical Clustering From Few Examples

Classical clustering methods usually return either a finite partition of the observed data or a finite dendrogram over it. This finite-sample view is inadequate when the hierarchy of interest is a recursive geometric object with fine-scale refinements that continue beyond the levels directly observed. We introduce classification fields: infinite-depth hierarchical cluster structures on Rd\mathbb{R}^d generated by a local parent-to-child refinement rule. A classification field generator maps each parent centre to an ordered, bounded, and separated tuple of child residuals. Together with a root and a scale factor, this rule recursively generates cluster centres, Voronoi cells, and a metric DAG encoding the hierarchy. Given only a finite prefix of such a hierarchy, we learn a classification field predictor that approximates the generator and can be rolled out to unseen depths. We prove exponential truncation convergence in the completed cell metric and ReLU realizability with width O(ε−γ)O(\varepsilon^{-γ}) and depth O~(ε−3γ/2)\widetilde O(\varepsilon^{-3γ/2}), where γ=log⁡K/(−log⁡s)γ=\log K/(-\log s), up to finite-window aspect-ratio factors. The approximation holds at the level of the induced compact metric structures, measured in the completed cell-metric Hausdorff distance. Experimental validation on matched CFG-generated hierarchies, IFS fractals, and image-induced recursive clustering hierarchies shows that learned predictors preserve ordered child slots, unordered geometry, and hierarchy-level path metrics under recursive rollout. These results support the claim that finite hierarchical observations can reveal local refinement rules capable of generating substantially deeper classification fields.

Yicen Li, Ruiyang Hong, Anastasis Kratsios +2

Department of Mathematics and Statistics, McMaster University, Canada · Vector Institute, Canada · University of Cambridge, United Kingdom

Hierarchical ClassificationClusteringHierarchical ClusteringHierarchical Representation Learning
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