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.

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347 papers33 papers in the last four weeks, up 18% on the four weeks before. 0.2% of all new papers.

Jun 19, 2026

Event Ontology Expansion via LLM-Based Conceptualization

Event ontology expansion aims to discover emerging event types from data and extend them to appropriate positions in the existing event ontology.. Existing methods typically cluster contextualized trigger representations and attach induced clusters to the ontology based on instance-level similarity. However, ontology expansion requires concept-level semantics that characterize event types, whereas contextualized trigger representations often conflate these semantics with surface contextual variation, leading to unstable clustering and unreliable hierarchy expansion. To address this issue, we propose ConceptE, a conceptualization-enhanced framework for event ontology expansion. ConceptE first derives concept-level semantics by prompting an LLM with the sentence and event trigger, producing a concise concept name and a natural-language description. It then jointly encodes these semantics with trigger information to build concept-enhanced representations aligned with ontology-level reasoning. This representation design supports more coherent event clustering, more reliable hierarchy expansion, and ontology-consistent type naming. Experiments on ACE, ERE, and MAVEN demonstrate that ConceptE consistently outperforms state-of-the-art approaches across all subtasks of event ontology expansion. In particular, it achieves improvements of up to 12.37% in BCubed-F1 for event clustering and 6.48% in Taxo_F1 for hierarchy expansion, demonstrating the effectiveness of the proposed ConceptE method.

Weicheng Ren, Zixuan Li, Long Bai +3

State Key Laboratory of AI Safety · Institute of Computing Technology, Chinese Academy of Sciences

ClusteringOntology Learning
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Jun 18, 2026

Eigenspace-Based Clustering for Personalized System Identification

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

Abdulmoneam Ali, Dipankar Maity, Ahmed Arafa

Department of Electrical and Computer Engineering University of North Carolina at Charlotte, NC 28223

ClusteringUnsupervised ClusteringSystem Identification
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Jun 17, 2026

FOSC-X: An Extended Framework for Optimal Local Cuts and Non-Horizontal Cluster Selection from Clustering Hierarchies

Extracting a flat clustering solution from a hierarchy is a common task in practical cluster analysis and can be formulated as an optimisation problem. Existing approaches focus on finding a single optimal solution. We introduce FOSC-X, a framework for extracting the top-M globally optimal flat clusterings from local, non-horizontal cuts of a hierarchical cluster tree, while optionally enforcing constraints on the number of clusters. This enables automatic identification of multiple high-quality alternative clusterings that capture different aspects of the hierarchical structure. Without constraints, the top-M problem can be solved in polynomial time using dynamic programming, exploiting the property that locally optimal partial candidates within subtrees can be combined to form globally optimal solutions while automatically determining the number of clusters. However, this can lead to solutions with numbers of clusters that are ultimately undesirable -- e.g., too large to be meaningful or practically analysed within a particular application domain. Imposing cluster-count constraints breaks the optimality property underlying the unconstrained dynamic programming approach, since locally optimal partial candidates may no longer combine into feasible globally optimal solutions. FOSC-X addresses this challenge through a dynamic programming strategy that maintains compact sets of feasible candidates using lower and upper feasibility bounds while pruning infeasible or dominated combinations. The resulting method guarantees optimal rankings of the top-M solutions with linear-time complexity in the number of cluster nodes and dataset size, both with and without cluster-count constraints. Experiments show that FOSC-X efficiently reveals alternative clustering structures overlooked by single-solution extraction methods.

Connor Simpson, Ricardo J. G. B. Campello

Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark.

Dynamic ProgrammingClusteringHierarchical ClusteringConstrained Optimization
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Jun 17, 2026

C-ARC: Continuous-Adaptive Range Clustering for Non-Repetitive LiDAR Sensors

Real-time LiDAR clustering identifies structures in point clouds, which is an essential prerequisite for many mobile robotics algorithms. Current methods are mostly developed for repetitive mechanical LiDAR sensors. Recently, the use of non-repetitive LiDAR sensors is strongly increasing due to their small cost and form factor. Such non-repetitive Risley prism-based sensors violate two key assumptions of repetitive mechanical sensors: structured scan lines and well-defined frame boundaries. Their Rhodonea-curve trajectories produce non-uniform point distributions, and the absence of a rotation cycle renders conventional scan line indexing inapplicable. To meet such new requirements, we developed C-ARC, a Continuous-Adaptive Range Clustering framework that maintains a persistent dual-graph over a sliding window, decoupling high-frequency point insertion from on-demand cluster retrieval. This is crucial for key functionalities like SLAM or tracking. An adaptive range grid resolution mechanism calibrates grid dimensions at initialization using an exponential control loop, balancing the sparsity-collision trade-off without prior knowledge of the scanning pattern. Implemented as an open-sourced single-threaded C++17 library, C-ARC produces real-time cluster output at 20 Hz on commodity hardware for the Livox Mid-360. Evaluation on the Livox Avia identifies unbounded cell occupancy as the primary limitation for sensors with strongly concentrated scan patterns. The adaptive resolution mechanism additionally improves clustering quality for existing grid-based methods on non-repetitive data.

Nick B. Schroeder, Jonathan Lichtenfeld, Oskar von Stryk

Technical University of Darmstadt, Darmstadt, Germany · Technical University of Darmstadt, Hochschulstr. 10, 64289 Darmstadt, Germany. · Simulation, Systems Optimization and Robotics Group, Technical University of Darmstadt, Darmstadt, Germany +1

ClusteringPoint Cloud Understanding
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Jun 17, 2026

Seed-Guided Semi-Supervised Clustering by A-Contrario Anomaly Detection

This paper introduces a semi-supervised clustering framework grounded in the statistical duality between grouping principles and anomaly detection. We address the challenge of robust cluster definition in noisy environments -- a task where partitioning algorithms often over-assign outliers and density-based methods remain sensitive to heuristic global parameters. Drawing on a-contrario statistical reasoning and Gestalt proximity principles, we define a cluster as a maximal subset of data points containing no anomalies relative to a null hypothesis of uniform randomness. Central to this approach is the Perception algorithm, which utilises a principled expectation-based threshold (E<1\mathbb{E} < 1) to identify outliers without manual parameter tuning. By treating clustering as the dual of anomaly detection, we employ an iterative ``clustering-by-exclusion'' mechanism. The algorithm is seed-guided, leveraging minimal user-provided labels to initialise robust cluster medians and form initial groups, which are subsequently expanded by admitting non-anomalous points. This approach naturally isolates fringe points, isolated noise, and emerging unknown clusters. We evaluate the method on synthetic and real-world benchmarks, including image and text datasets represented through raw, linear-reduced, and neighbourhood-preserving embeddings. Results demonstrate that with as few as 10--30 seeds per cluster, the proposed method achieves competitive and often very strong performance under a practical low-tuning benchmarking protocol, while maintaining linear scalability with respect to both observations and dimensionality for a fixed number of seeded clusters and iterations.

Nassir Mohammad

Cyber Innovation Lab, Airbus, Newport, UK

ClusteringSemi-Supervised Learning
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Jun 17, 2026

S-JEPA : Soft Clustering Anchors for Self-Supervised Speech Representation Learning

Self-supervised speech encoders are predominantly trained by predicting discrete hard cluster IDs at masked positions, a recipe that collapses acoustic ambiguity at category boundaries and requires interrupting training to re-cluster the entire corpus between iterations. We introduce S-JEPA, a JEPA-style encoder-predictor pair trained to match the soft posteriors of a Gaussian Mixture Model at masked positions via KL divergence. Training runs as one continuous optimization trajectory in two phases: a fixed GMM over MFCC features, then an online GMM over encoder features, with the input layer selected adaptively from a label-free signal, removing both the offline re-cluster step and the hand-tuned choice of which transformer layer to cluster on. Under the SUPERB protocol, S-JEPA achieves the lowest WER among evaluated SSL methods below 90M parameters and matches HuBERT-Base on emotion recognition at roughly half its parameter count, establishing a new Pareto frontier without offline re-clustering or teacher distillation. An analysis of the predictor's per-frame entropy on held-out speech reveals a bimodal distribution with a substantial minority of frames near the entropy of a perfect two-cluster tie, providing direct empirical evidence that the soft-target objective preserves the acoustic ambiguity that hard targets would collapse. Code is available at https://github.com/gioannides/s-jepa.

Georgios Ioannides, Adrian Kieback, Judah Goldfeder +5

Carnegie Mellon University · James Silberrad Brown Center for AI · Amazon GenAI +4

ClusteringJoint-Embedding Predictive ArchitectureSelf-Supervised Speech Representation Learning
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Jun 17, 2026

scGTN: Deep Siamese Graph Transformer Network for Single-cell RNA Sequencing Clustering

Single-cell RNA sequencing (scRNA-seq) serves a pivotal role in characterizing gene expression at the cellular level, enabling the identification of cell types and advancing the understanding of cellular heterogeneity. Despite the significant progress in scRNA-seq data clustering, we argue that current methods always ignore the sparsity and noise, as well as the complex intercellular structural information inherent in scRNA-seq data. Toward this end, in this paper, we propose a novel single-cell RNA-seq clustering framework via deep Siamese Graph Transformer Network (termed scGTN), which explicitly integrates gene expression profile and intercellular structural dependencies for cell clustering. In particular, we formulate scRNA-seq data as a graph and construct two augmented graph views that serve as dual views to capture complementary intercellular information. Then, a Siamese graph transformer network is employed to explicitly incorporate shortest-path information and node-wise distances for capturing richer structural relationships between cells. Finally, we employ an optimal transport strategy to guide the cell clustering in a self-supervised manner. Extensive experiments on multiple benchmark scRNA-seq datasets demonstrate that our scGTN consistently outperforms existing methods. Our code is available at https://github.com/W-RMSL/scGTN.

Jinke Wu, Yifan Wang, Siyu Yi +5

Sichuan University · University of International Business and Economics · Great Bay University +1

Graph SSLClusteringGraph ClusteringGraph TransformerSingle-Cell RNA Sequencing
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Jun 12, 2026

Cluster LOCO: Feature Importance For Interpreting Clusters

Clustering is widely used for exploratory analysis and scientific discovery, driving insights from market segmentation to biological data analysis, but its outputs can be difficult to interpret, audit, and reproduce as modern datasets become increasingly large and complex. Reliable use of clustering requires understanding which features drive the discovered structure, yet feature-level explanations for clustering remain scarce compared with methods in supervised learning. Furthermore, existing clustering feature importance scores are often tied to specific algorithms and data assumptions. To address these challenges, we propose Cluster LOCO (Leave-One-Covariate-Out), a family of model-agnostic feature importance scores for clustering. Cluster LOCO is built on feature occlusion and clustering generalizability, defined as whether cluster labels learned on one subset of the data can be accurately predicted on held-out samples. For any chosen clustering algorithm, Cluster LOCO quantifies a feature's importance by measuring how much its removal degrades generalizability. We first introduce Cluster LOCO-Split, which relies on data splitting, and then extend it to Cluster LOCO-MP, a minipatch ensemble-based version designed for large-scale data. Across synthetic simulations and an application to cell-type discovery in single-cell transcriptomics, we show that Cluster LOCO more reliably recovers informative features than existing clustering feature importance methods.

Claire M. He, Genevera I. Allen

Department of Statistics · Columbia University · New York, NY 10027, USA

Clustering
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Jun 11, 2026

Robust State-Conditional Feature-Weighted Jump Models for Temporal Clustering

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

Federico P. Cortese, Alessio Farcomeni

University of Milan, Department of Economics, Management, and Quantitative Methods · National Research Council of Italy, Institute for Applied Mathematics and Information Technologies, Milan · University of Rome “Tor Vergata”, Department of Enterprise Engineering

ClusteringUnsupervised ClusteringFeature SelectionTime Series Clustering
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Jun 11, 2026

scLLM-DSC: LLM-Knowledge Enhanced Cross-Modal Deep Structural Clustering for Single-Cell RNA Sequencing

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

Ping Xu, Pengjiang Li, Tian Du +6

Computer Network Information Center, Chinese Academy of Sciences, Beijing, China · University of Chinese Academy of Sciences, Beijing, China · School of Computing and Information Technology, Great Bay University, Dongguan, China +2

ClusteringUnsupervised ClusteringMultimodal EmbeddingSingle-Cell RNA Sequencing
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Jun 10, 2026

Efficient Time Series Clustering from Multiscale Reservoir Dynamics with Granular-Ball Anchoring Graph Optimization

Time-series clustering remains challenging due to the inherent trade-off between clustering effectiveness and computational efficiency. Similarity-based methods often suffer from quadratic complexity caused by pairwise distance computations, while deep learning-based approaches typically rely on costly iterative training and a large number of trainable parameters. In this paper, we propose MSRGC-Net, an efficient time-series clustering framework that integrates multiscale reservoir computing, granular-ball-based anchoring graph construction, and consensus learning. MSRGC-Net adopts a training-free reservoir computing paradigm to extract multiscale temporal representations from raw time series without backpropagation, significantly reducing computational overhead. To capture the intrinsic structure of the resulting representations, granular-ball computing is employed to adaptively model data distributions via density-consistent regions, yielding compact and robust anchor graph representations. Furthermore, a consensus-based anchoring graph optimization strategy is introduced to effectively align multiscale reservoir representations and integrate complementary information across temporal scales. Extensive experiments on widely used univariate and multivariate benchmark datasets demonstrate that MSRGC-Net consistently outperforms state-of-the-art methods in clustering performance while maintaining superior computational efficiency.

Yifan Wang, Lifeng Shen, Shuyin Xia +1

Chongqing Key Laboratory of Computational Intelligence, Key Laboratory of Cyberspace Big Data Intelligent Security, Ministry of Education, Sichuan-Chongqing Co-construction Key Laboratory of Digital Economy Intelligence and Key Laboratory of Big Data Intelligent Computing, College of Computer Science and Technology, Chongqing University of Posts and Telecommunications · Chongqing Ant Consumer Finance Co,. Ltd, Ant Group.

ClusteringTime Series Clustering
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Jun 10, 2026

Towards Data-free and Training-free Compression for Speech Foundation Models Using Parameter Clustering

This paper presents a novel data-free and training-free compression approach for speech foundation models using channelwise clustering via k-means. More fine-grained, mixed sparsity pruning by layer-level varying number of parameter clusters is also explored. Experiments conducted on the LibriSpeech dataset suggest that when operating with pruning sparsity of 50% on HuBERT-large, consistent WER reductions of 27.73%/18.61% absolute (34.37%/21.91% relative) over the magnitude-based pruning were obtained on the test-clean and test-other subsets before fine-tuning and 0.19%/0.79% absolute (3.36%/4.62% relative) after fine-tuning with only 3 epochs. Similar WER reductions of 2.86%/5.02% absolute (59.21%/55.29% relative) were observed against magnitudebased pruning on Whisper-large-v3 at 10% sparsity, all with no significant WER increase relative to the uncompressed baseline.

Haoning Xu, Zhaoqing Li, Huimeng Wang +4

The Chinese University of Hong Kong, Hong Kong SAR, China · National Research Council Canada, Canada

Speech Foundation ModelsClusteringSpeech ProcessingNeural Network CompressionNeural Network Pruning
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Jun 9, 2026

Flash-GMM: A Memory-Efficient Kernel for Scalable Soft Clustering

We present Flash-GMM, a fused Triton kernel for efficient computation of Gaussian Mixture Models (GMMs) over large-scale data in a single GPU pass. By eliminating the need to materialize the full responsibility matrix in GPU memory, Flash-GMM achieves a \textbf{20×\times} speedup over existing implementations and enables training on datasets more than \textbf{100×\times} larger than previously feasible on one device. To demonstrate its impact, we integrate Flash-GMM into the IVF coarse quantizer for approximate nearest-neighbor (ANN) search. We show that soft GMM clustering is now a viable drop-in replacement for kk-means, and that GMM responsibilities can be leveraged to assign border vectors to multiple clusters. Our approach reaches fixed recall targets with up to 1.7×1.7\times fewer distance computations, or equivalently, yields +2+2--1212 recall@10 at matched computational cost. We release the kernel as an open-source project.

Gal Bloch, Ariel Gera, Matan Orbach +2

IBM Research

GPU Kernel OptimizationGPU AccelerationHigh-Performance ComputingClusteringGaussian Mixture Models
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Jun 9, 2026

Recovering the Zipfian Distribution in Unsupervised Term Discovery

Unsupervised term discovery involves segmenting unlabelled speech into word- or syllable-like units and clustering these into a lexicon of candidate types. True lexicons follow a Zipfian distribution, yet the dominant centre-based clustering approach -- K-means -- produces a more uniform distribution due to an inductive bias toward spherical clusters. In this paper we revisit graph-based clustering as a bottom-up alternative, where segment embeddings are connected by pairwise similarity and partitioned using the Leiden algorithm. We show that graph clustering substantially outperforms centre-based approaches (K-means, GMM, BIRCH) in both word- and syllable-level lexicon discovery across three languages, producing more Zipf-like distributions. Another bottom-up approach, agglomerative clustering with average linkage, also performs well, although it is computationally less efficient and allows for less control over the resulting distribution. Our work calls into question the dominance of centre-based clustering for term discovery, and promotes graph clustering as an attractive alternative.

Danel Slabbert, Simon Malan, Herman Kamper

Electrical and Electronic Engineering, Stellenbosch University, South Africa

Zipf's LawClusteringHierarchical ClusteringGraph Clustering
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Jun 9, 2026

ClusBench: The Clustering Benchmark Data Resource You've All Been Waiting For (?)

Although some very common test beds exist for assessing the performance of clustering methods, large scale benchmarking is typically limited to relatively simplistic simulation set-ups. Here we describe the production and curation of close to 3000 synthetic data sets, derived from more than 200 publicly available data sets; the majority of which arose from real-world applications. By fitting a flexible non-parametric distribution to each base data set we are able to retain much of the nuance in real-world data which is difficult to reproduce in standard simulations, while also producing data sets whose sizes are sometimes substantially greater than the data sets from which they are derived. The synthetic data sets, plus an accompanying R package, are available for download from https://github.com/DavidHofmeyr/ClusBench.

David P. Hofmeyr

School of Mathematical Sciences, Lancaster University

Benchmark ConstructionClusteringSynthetic Data GenerationSynthetic Benchmark Generation
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Jun 8, 2026

Joint user-item allocation for e-commerce marketing campaigns

Web platforms run many marketing campaigns at once, and for each one they must decide which products to promote and which users to target. The best users depend on the products, and the best products on the users. The campaigns also compete with one another, because each user and each item may belong to only one of them and each audience is capped by the campaign budget. Still, existing approaches fix one side and search the other, choosing an assortment and then looking for its audience, or ranking items for one user at a time. Either way they solve a restricted version of the full problem, implying that a jointly optimized assignment would be at least as good and possibly far better. What the restriction costs, and whether the joint problem is solvable at the scale campaigns are run, remain unknown. Here we formalize the joint task as auto-targeting: assigning users and items to multiple disjoint, capacity-bounded campaigns that maximize the affinity between them. We adapt constrained spectral biclustering, greedy local search with pairwise swaps, and a multi-armed bandit formulation to the task and compare them against the conventional decoupled baseline. On synthetic data, two Amazon Reviews benchmarks, and two proprietary commercial datasets, auto-targeting raises campaign lift over the best decoupled pipeline, from around 20% on the two smaller, denser datasets to more than threefold on the two largest. Biclustering yields the highest campaign quality across datasets, while bandit-based methods run fastest on the largest ones.

Maja Lindström, Natalija Glisovic, Jan von Pichowski +2

Department of Computing Science Integrated Science Lab Umeå University SE-901 87 Umeå, Sweden · KTH Royal Institute of Technology Stockholm, SE-114 28, Sweden · Chair of Machine Learning for Complex Networks Center for Artificial Intelligence and Data Science (CAIDAS) University of Würzburg DE-97070 Würzburg, Germany +2

Clustering
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Jun 8, 2026

Closure-Validated Circuit Discovery in Attention Heads: Co-activation Proposes, Ablation Disposes

Interpretability increasingly treats groups of components, not individual units, as the basic object, and proposes to find them by clustering co-activation statistics. We ask whether such a cheap signal actually identifies an attention-head circuit. Adapting a sparse-autoencoder clustering recipe to attention heads -- but validating by causal ablation rather than reconstruction -- we cluster heads and then run a closure test: ablate the discovered community and compare per-example damage to matched-random controls. Across two dense 1B-scale models (Pythia 1B, OLMo 1B) and two input distributions, the communities pass closure. In a Mixture-of-Experts model (OLMoE-1B-7B), route-conditional clustering recovers a statistically real signal that nonetheless does not survive closure -- ablation improves loss, the wrong direction. Extending closure across training, attention-target selectivity and participation ratio decouple from function in both directions. We conclude that a cheap signal is a circuit proposal, not a confirmed circuit; closure is what separates them.

Yongzhong Xu

Transformer InterpretabilityCircuit DiscoveryAttention Head AnalysisClusteringMulti-Head Attention
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Jun 8, 2026

Alcmean's: Unsupervised community detection using local Laplacian, automatic detection of the number of centers

Community detection is a fundamental problem in the analysis of complex networks. It has applications across social, biological, and financial domains. Traditional algorithms such as Louvain, LPA, and modularity optimization often require manual parameter tuning. They also suffer from inaccurate cluster center selection and struggle with scalability. To address these challenges, we propose Automatic Laplacian Centrality Means (ALCMeans), a novel community detection algorithm. ALCMeans combines Laplacian energy-based automatic center identification with DeepWalk embeddings for robust node representation. Unlike existing Laplacian-based and clustering methods, ALCMeans eliminates the need to predefine the number of communities, enhances cluster center selection using structural importance, and leverages representation learning for more accurate and stable assignments. Experimental results on benchmark datasets demonstrate 10 to 20 percent higher NMI and ARI scores compared to Louvain, Newman-Girvan, LPA, Fast-Greedy, and a recent GNN-based competitor (MAGI, KDD 2024). Additional evaluations with modularity and F1-scores confirm the superiority of ALCMeans. Ablation studies highlight the critical contributions of each component. Despite its reliance on DeepWalk parameters and increased runtime relative to lightweight heuristics, ALCMeans consistently outperforms state-of-the-art methods. This makes it a promising tool for real-world network analysis.

Shahin Momenzadeh, Rojiar Pir Mohammadiani

Department of Computer Engineering, University of Kurdistan, Sanandaj, Iran

Cluster Number EstimationClusteringGraph Clustering
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Jun 6, 2026

Orthogonality and Dimensionality in Airline Cluster Analysis using PCA and Kernel PCA

This methodological study analyzes the effects of collinearity, effective dimensionality, and cluster stability in a 2023 study of US airline profit cycles from 1995 to 2020 by Renold et al., which uses k-means clustering, principal component analysis, and system dynamic modelling.We replicate their clustering experiment in three spaces -- the original 7-dim. raw-variable space, a 3-dim. PC score space, and a 4-dim. PC score space using their dataset. We show that the six-cluster taxonomy is geometrically robust: k-means in 3-PC space produces bit-for-bit identical cluster assignments relative to 7D raw space. As a nonlinearity check we apply kernel PCA under six kernels spanning three families plus a linear baseline. The kernels confirm an intrinsically linear manifold with no detectable curvature. The silhouette criterion reveals that the dataset structurally supports only three clusters, not six. Collinearity in the raw 7D space suppresses the silhouette signal. A kernel ridge regression check confirms no nonlinear accuracy gain over linear ridge once the COVID19 year is excluded. Together, these results argue for clustering on PC scores rather than raw variables in collinearity-prone panel data.

Andreas Schlapbach

Swiss Federal Railways (SBB), Switzerland

Intrinsic DimensionalityPrincipal Component AnalysisClustering
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Jun 5, 2026

Unsupervised Continual Clustering via Forward-Backward Knowledge Distillation

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

Mohammadreza Sadeghi, Sareh Soleimani, Zihan Wang +1

Department of Electrical and Computer Engineering, McGill University, Montreal, QC H3A 0E9, Canada · Mila – Quebec AI Institute, Montreal, QC H2S 3H1, Canada

ClusteringUnsupervised ClusteringKnowledge DistillationCatastrophic Forgetting
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Jun 3, 2026

Sparse Functional Singular Value Decomposition for Biclustering and Triclustering Longitudinal Data

Identifying subtypes of complex conditions, such as Inflammatory Bowel Disease (IBD), often requires capturing latent patterns in longitudinal omics data. However, these data are typically high-dimensional, sparsely sampled, and irregularly observed over time, posing substantial challenges for conventional (bi)clustering and functional data analysis methods. We propose Tri-SfSVD, a unified sparse functional Singular Value Decomposition framework for discovering biclusters and triclusters in longitudinal data. Unlike existing functional biclustering methods that rely on ad hoc imputation or enforce restrictive shape-homogeneity assumptions, Tri-SfSVD integrates continuous trajectory estimation with simultaneous subject, feature, and temporal selection within a single optimization framework. By imposing sparse penalties across subjects, variables, and temporal subregions, the proposed method works directly on observed data to uncover localized structures at the subject, subject-feature, and subject-feature-time levels. Extensive simulations demonstrate that Tri-SfSVD outperforms existing approaches in high-dimensional settings. Applied to IBD multi-omics data, the method identified three biclusters linking sample clusters with distinct IBD-related clinical characteristics to microbial pathway groups associated with specific bacterial taxa, providing interpretable subject-pathway associations for characterizing disease heterogeneity. Applied to multi-channel EEG data, the method identified three triclusters linking sample clusters with distinct alcohol-related phenotypes to localized brain activity patterns, including subgroup differences separated by temporal subregions within the same spatial region.

Yue Zhao, Thierry Chekouo, Sandra Safo

Division of Biostatistics and Health Data Science University of Minnesota 2221 University Avenue SE2026 Minneapolis, MN 55414, United States

Functional Data AnalysisClusteringSingular Value Decomposition
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Jun 3, 2026

UniFair: A unified fair clustering approach based on separation and compactness

Clustering is increasingly used to support high-impact decisions, yet standard objectives such as k-means can produce clusterings that treat demographic groups unequally. Existing fair clustering methods typically optimize a single notion of fairness and often overlook how clustering costs interact with the geometry of the induced decision boundaries. We propose UniFair, a unified framework that jointly optimizes separation fairness and social fairness. Separation fairness encourages protected groups to lie farther from the induced decision boundaries, while social fairness reduces disparities in within-cluster distortion by penalizing group-wise clustering costs. We develop gradient-based optimization procedures for separation-fair and unified k-means objectives, and extend them to deep clustering by enforcing the same criteria in the latent space of an autoencoder. Experiments on tabular and image datasets show that UniFair reduces both boundary-related and cost-based group disparities with only a modest increase in clustering loss.

Antonia Karra, Vasiliki Papanikou, Georgios Vardakas +2

University of Ioannina, Greece · Archimedes/Athena Research Center, Greece

ClusteringAlgorithmic FairnessDeep ClusteringGroup Fairness
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Jun 3, 2026

Robust Multi-view Clustering against Imperfect Information

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

Zhichao Huang, Haochen Zhou, Hao Wang +2

College of Computer Science, Sichuan University, China. · School of Artificial Intelligence, Sichuan University, China. · Tianfu Jincheng Laboratory, Chengdu, China.

ClusteringMulti-View LearningUnsupervised ClusteringMulti-View Clustering
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Jun 2, 2026

Central Description Length (CDL) Clustering Validation Index

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

Mahdi Shamsi, Soosan Beheshti

Toronto Metropolitan University, 350 Victoria St., Toronto, Ontario M5B 2K3, Canada

Minimum Description LengthClusteringUnsupervised ClusteringCluster Number Estimation
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Jun 1, 2026

Semi-Supervised Hyperbolic Hierarchical Clustering with Set-Level Structural Priors

Semi-supervised hierarchical clustering aims to learn a tree structure consistent with data patterns and user-provided supervision. Supervision is usually given as leaf-level relations, such as pairwise must-link/cannot-link constraints or triplet-wise must-link-before constraints. Although useful for regulating local sample relations, such supervision does not directly indicate which samples should form coherent subtrees. Consequently, the non-leaf structure of the learned tree may deviate from the hierarchical organization preferred by ground-truth labels. To address this limitation, we propose a semi-supervised hyperbolic hierarchical clustering method with set-level structural priors. The main contribution is to introduce sets as basic modeling units for hierarchy learning. Each set denotes samples expected to cohere within a subtree and is induced from leaf-level supervision together with a learned constraint-consistent similarity structure. These sets act as soft structural priors for subtree-level supervision, allowing supervision to guide non-leaf hierarchy formation beyond local leaf-level relations. Specifically, we first learn constraint-consistent embeddings to obtain a reliable set partition, then construct constraint-induced sets and estimate inter-set similarities to form set-level structural priors. Finally, these priors are incorporated into a hyperbolic hierarchy objective for continuous tree optimization. Experiments on eleven benchmark datasets and ablation studies show that the proposed method consistently improves label consistency over representative hierarchical clustering baselines while also enhancing similarity-based tree quality.

Junjing Zheng, Xinyu Zhang, Xiangfeng Qiu +2

College of Electronic Science and Technology, National University of Defense Technology, Changsha 410073, China

ClusteringHierarchical ClusteringSemi-Supervised Learning
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May 31, 2026

Agentic Clustering: Controllable Text Taxonomies via Multi-Agent Refinement

Recent text-clustering methods use large language models to propose a cluster taxonomy from a corpus and then assign each text to it. These pipelines are fundamentally programmatic: the sequence of LLM calls and the rules for stopping, merging, and splitting clusters are fixed in code in advance, so they generalise poorly across corpora of different structure and cannot easily incorporate user-supplied constraints such as a target cluster count or a clustering intent. We propose an agentic alternative in which an orchestrator LLM inspects the state of the discovery process at each step and dispatches one of a small set of specialised agents -- proposer, synthesizer, auditor, investigator, and critic -- adapting the pipeline to the corpus rather than executing a fixed one. On seven public text-clustering benchmarks the method achieves state-of-the-art performance, beating the strongest prior baseline by 47% in mean ARI.

Simon Löwe, Emily Silcock

Burning Glass Institute · Harvard University

Multi-Agent LLM SystemsClusteringLLM Agent OrchestrationText ClusteringSemantic Clustering
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May 29, 2026

PE-means: Improved Differentially Private kk-means Clustering through Private Evolution

We study the problem of differentially private (DP) kk-means clustering in Euclidean space. Previous solutions rely on summing the private data directly, which induces a sensitivity proportional to the domain. We introduce PE-means, an extension of the private evolution (PE) algorithm (an increasingly popular method for synthetic data generation), to the problem of kk-means clustering. The key advantage of PE is that it only computes a private histogram with constant sensitivity to guide the evolution. Our adaptation of PE includes new evolutionary operators for clustering, as well as other algorithmic improvements of independent interest. Overall, PE-means achieves an average improvement of 26% in clustering loss over state-of-the-art baselines such as Google's LSH-based algorithm and DP-Lloyd variants.

Thomas Humphries, Zinan Lin, Sergey Yekhanin

University of Waterloo · Microsoft Research

ClusteringPrivacy-Preserving MLDifferential Privacy
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May 29, 2026

Cluster Analysis with Resampling for Validation and Exploration (CARVE)

Clustering is widely used across the sciences as the foundation for downstream data-driven scientific discoveries. However, clustering results are highly sensitive to the choice of algorithm, preprocessing, and the number of clusters kk, producing scientific claims that are often not reproducible. The current state of the art for validating clustering solutions consists of clustering validation indices (CVIs) such as Silhouette, Davies-Bouldin, and Calinski-Harabasz, which rely on geometric assumptions that break down on the heavy-tailed, high-dimensional, and nonlinearly structured data encountered in biomedical research. Resampling-based alternatives - grounded in the ideas of clustering stability and generalizability - have been proposed but remain scattered across specialized tools with no unified, accessible software. We fill this gap with CARVE (Cluster Analysis with Resampling for Validation and Exploration), an open-source Python and R package that jointly evaluates multiple clustering algorithms and hyperparameters, returning stability and generalizability diagnostics at the global, cluster, and sample level together with principled selection rules and consensus-based cluster labels. Across six synthetic benchmarks CARVE consistently recovers near-optimal clusterings where classical indices degrade substantially. On experimental genomics and proteomics data sets, CARVE recovers finer biological structure when classical CVIs collapse entirely. CARVE is available with a scikit-learn-compatible Python API and an analogous R interface compatible with Seurat workflows.

Kai R. Wycik, Tiffany M. Tang, Tarek M. Zikry +1

Department of Statistics, Columbia University, New York, NY, USA · Center for Theoretical Neuroscience, Zuckerman Mind Brain Behavior Institute, Columbia University, New York, NY, USA · Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, USA +2

ClusteringScientific Reproducibility
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May 29, 2026

ERICA: Quantifying Replicability of Cluster Analysis

Despite being ubiquitous in science, clustering lacks a unified framework for quantitatively evaluating the replicability of its results. We present evaluating replicability via iterative clustering assignments (ERICA), a method for determining whether clusters can be identified reproducibly in a dataset. The pipeline computes a statistic that determines whether reproducible cluster structure is present in a dataset. Quantitative visualization methods are also introduced to characterize similarities between clusters and identify observations that may represent outliers or unstable assignments. Experiments on synthetic datasets demonstrate that ERICA successfully identifies reproducible cluster structure. In contrast, application of ERICA to three breast cancer gene-expression datasets reveals instances in which clustering solutions are not reproducible. The study underscores the importance of rigorously evaluating clustering solutions and provides a practical framework for doing so.

Siamak K. Sorooshyari, Manuel A. Rivas, Robert Tibshirani

Department of Statistics Stanford University Stanford, CA 94305, USA · Department of Biomedical Data Science Stanford University Stanford, CA 94305, USA · Department of Statistics and Biomedical Data Science Stanford University Stanford, CA 94305, USA

ClusteringML ReproducibilityScientific Reproducibility
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May 29, 2026

Mathematical Morphology in Machine Learning

This work introduces mathematical morphology-an established visual computing theory-into machine learning to exploit shape and density aspects often overlooked by standard techniques. We propose a fast clustering algorithm based on morphological reconstruction that accurately preserves cluster shapes and density. This scheme offers unique features: an intrinsic sense of maximal clusters, cost-free noise removal, and diverse growth patterns controlled by structuring elements.Additionally, we propose a novel distance metric combining Minkowski and Chebyshev distances, highly efficient for morphological dilations. In Z2Z^2 discrete neighbourhood iterations, it is roughly 1.3 times faster than Manhattan and 329.5 times faster than Euclidean distances. When evaluated using a k-Nearest Neighbours (k-NN) classifier across 33 UCI datasets against 14 other distances, our metric achieved above-average accuracies most frequently (26 of 33 cases) and the best overall accuracy in 9 cases.Finally, we introduce novel morphological classifiers. Unlike current literature, this proposal uniquely models shape, density, and fractal information in datasets.

Erick Oliveira Rodrigues, Aura Conci

®Universidade Federal Fluminense

Clustering
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