Unsupervised Clustering

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11 papers in the last four weeks, against 2 the four weeks before. 0.1% of all new papers.

Jul 13Week of Sep 28

Latest papers 85

May 23, 2026stat.ML

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 Finance Clustering Unsupervised Clustering

May 18, 2026cs.AI

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 Optimization Metaheuristic Optimization Clustering Unsupervised Clustering

May 13, 2026stat.ML

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

K

-means,

K

-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

Amortized Inference Clustering Unsupervised Clustering Time Series Clustering

May 12, 2026cs.LG

Information theoretic underpinning of self-supervised learning by clustering

Self-supervised learning (SSL) is recognized as an essential tool for building foundation models for Artificial Intelligence applications. The advances in SSL have been made thanks to vigorous arguments about the principles of SSL and through extensive empirical research. The aim of this paper is to contribute to the development of the underpinning theory of SSL, focusing on the deep clustering approach. By analogy to supervised learning, we formulate SSL as K-L divergence optimization. The mode collapse is prevented by imposing an optimisation constraint on the teacher distribution. This leads to normalization using inverse cluster priors. We show that using Jensen inequality this normalization simplifies to the popular batch centering procedure. Distillation and centering are common {heuristics-based} practices in SSL, {but our work underpins them theoretically.} The theoretical model developed not only supports specific existing successful SSL methods, but also suggests directions for future investigations.

Josef Kittler, Sara Atito, Muhammad Awais

Centre for Vision, Speech and Signal Processing (CVSSP), University of Surrey, Guildford, Surrey GU2 7XH, UK · Surrey Institute for People-Centred AI (PAI), University of Surrey, Guildford, Surrey GU2 7XH, UK

Self-Supervised Learning Unsupervised Clustering

May 9, 2026cs.LG

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

Clustering Unsupervised Clustering

May 9, 2026cs.LG

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

Clustering Unsupervised Clustering Adaptive Learning

May 8, 2026cs.SD

BeeVe: Unsupervised Acoustic State Discovery in Honey Bee Buzzing

Discovering structure in biological signals without supervision is a fundamental problem in computational intelligence, yet existing bioacoustic methods assume vocal production models or predefined semantic units, leaving non-vocal species poorly served. This work introduces BeeVe, an unsupervised framework for acoustic state discovery in collective honey bee buzzing. BeeVe uses the self-supervised Patchout Spectrogram Transformer (PaSST) as a frozen feature extractor, then trains a Vector-Quantized Variational Autoencoder (VQ-VAE) without labels on those embeddings, learning a finite discrete codebook of acoustic tokens directly from unlabelled hive audio. No labels, pretext tasks, or contrastive objectives are used at any stage. Post-hoc evaluation against known queen status reveals that the learned tokens separate queenright and queenless conditions with Jensen-Shannon Divergence values between 0.609 and 0.688, and that the queenless condition further decomposes into three internally coherent sub-states stable across experiments with different codebook sizes and random seeds. Token transition analysis confirms non-random sequential structure (p << 0.001) across all experiments. Generalisation to unseen recordings preserves both token overlap (Jaccard = 0.947) and global manifold topology. These results demonstrate that unsupervised discrete codebook learning can recover repeatable acoustic structure from a non-vocal biological signal without annotation, opening a path toward non-invasive acoustic hive health monitoring.

Hamze Hammami, Nidhal Abdulaziz

Audio Representation Learning Unsupervised Clustering Vector-Quantized Variational Autoencoder Bioacoustics

May 8, 2026cs.LG

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 Stability Clustering Unsupervised Clustering Mass Spectrometry

May 7, 2026q-bio.QM

An Explainable Unsupervised-to-Supervised Machine Learning Framework for Dietary Pattern Discovery Using UK National Dietary Survey Data

Clinical dietary assessment can generate detailed but high-dimensional nutrient and food-group information that is difficult to translate quickly into counselling priorities. This paper proposes an explainable unsupervised-to-supervised machine learning framework for discovering, reproducing and interpreting dietary patterns using public UK National Diet and Nutrition Survey data. Adult participants aged 19 years and above from NDNS Years 12-15 were represented using 25 energy-adjusted nutrient and food-group features. K-means, Gaussian Mixture Models and Agglomerative Clustering were compared across k = 2-8, with stability and dietetic interpretability used alongside internal validation metrics. The selected K-means k = 4 solution identified four interpretable dietary patterns: high fat/meat and sodium, higher fibre fruit-vegetable micronutrient, high free-sugar snacks and sugary drinks, and dairy/cereal calcium-rich saturated-fat. A supervised surrogate classifier reproduced held-out cluster membership with high test performance (macro-F1 = 0.963), but was interpreted only as an explanatory surrogate rather than as an independent clinical prediction model. SHAP analysis linked predictions to dietetically meaningful drivers, suggesting potential value for dietitian-in-the-loop assessment, counselling prioritisation and follow-up monitoring.

Wing Yi Yu, Chun Yin Chiu

School of Health Sciences, University of East Anglia, Norwich, United Kingdom · Department of Informatics, King's College London, London, United Kingdom

Clinical Decision Support Interpretable ML Unsupervised Clustering

May 1, 2026cs.LG

Towards Robust and Scalable Density-based Clustering via Graph Propagation

We present \textit{CluProp}, a novel framework that reimagines varied-density clustering in high-dimensional spaces as a label propagation process over neighborhood graphs. Our approach formally bridges the gap between density-based clustering and graph connectivity, leveraging efficient propagation mechanisms from network science to mitigate the parameter sensitivity inherent in traditional density-based methods. Specifically, we introduce a deterministic density-based propagation strategy to ensure scalable neighborhood identification. The framework is agnostic to the choice of distance metric and exhibits superior performance on large-scale data, processing millions of points in minutes while consistently outperforming existing baselines in accuracy.

Yingtao Zheng, Hugo Phibbs, Ninh Pham

School of Computer Science, University of Auckland, New Zealand. · Department of Mathematics and Computer Science, University of Southern Denmark, Denmark.

Clustering Unsupervised Clustering

Apr 25, 2026stat.ML

Turtle shell clustering: A mixture approach to discriminative clustering with applications to flow cytometry and other data

Generative approaches to clustering provide information on geometric properties of clusters, whereas discriminative approaches provide boundaries between clusters. Ideas from both approaches are incorporated to present a fully unsupervised, probabilistic, and discriminative clustering method via a regularized mutual information objective function, wherein a mixture of mixtures of Gaussian and uniform distributions is used for formulation of the conditional model. Automatic selection of the number of components is established with the introduction of the regularizing term and a merge step, similar to those applied in reversible jump Markov chain Monte Carlo methods used in Bayesian clustering. Consequently, the turtle shell method -- a fully unsupervised clustering method capable of estimating non-linear boundary lines, automatically selecting the number of components, and capturing intuitive clusters in the presence of data abnormalities such as noise and/or irregular cluster shapes -- is introduced. We test this method on various simulated and real datasets commonly explored in clustering research, and extend the analysis to datasets arising from flow cytometry experiments.

Mackenzie R. Neal, Paul D. McNicholas, Arthur White

Department of Mathematics & Statistics, McMaster University, Ontario, Canada · School of Computer Science & Statistics, Trinity College Dublin, Ireland

Clustering Gaussian Mixture Models Unsupervised Clustering

Apr 24, 2026cs.LG

Deep Clustering for Climate: Analyzing Teleconnections through Learned Categorical States

Understanding and representing complex climate variability is essential for both scientific analysis and predictive modeling. However, identifying meaningful climate regimes from raw variables is challenging, as they exhibit high noise and nonlinear dependencies. In this work, we explore the use of Masked Siamese Networks to discretize climate time series into semantically rich clusters. Focusing on daily minimum and maximum temperature, we show that the resulting representations: (i) yield clusters that reflect meaningful climate states under our modeling assumptions, offering a simplified representation for downstream use; (ii) enable sampling and analysis of specific climate scenarios; and (iii) exhibit statistical associations with El Niño events, underscoring their scientific relevance. Our findings highlight the potential of self-supervised discretization as a tool for climate data analysis and open avenues for incorporating richer climate indicators in future work.

Lívia Meinhardt, Dário Oliveira

FGV EMAp

Representation Learning Time Series Classification Climate Science Self-Supervised Time Series Representation Learning Unsupervised Clustering Time Series Clustering

Apr 23, 2026cs.LG

An effective variant of the Hartigan $k$ -means algorithm

The k-means problem is perhaps the classical clustering problem and often synonymous with Lloyd's algorithm (1957). It has become clear that Hartigan's algorithm (1975) gives better results in almost all cases, Telgarsky-Vattani note a typical improvement of

5\%

--

10\%

. We point out that a very minor variation of Hartigan's method leads to another

2\%

--

5\%

improvement; the improvement tends to become larger when either dimension or

k

increase.

François Clément, Stefan Steinerberger

Clustering Unsupervised Clustering

Apr 16, 2026cs.LG

An unsupervised decision-support framework for multivariate biomarker analysis in athlete monitoring

Purpose. Athlete monitoring is constrained by small cohorts, heterogeneous biomarker scales, limited feasibility of repeated sampling, and the lack of reliable injury ground truth. These limitations reduce the interpretability and utility of traditional univariate and binary risk models. This study addresses these challenges by proposing an unsupervised multivariate framework to identify latent physiological states in athletes using real data. Methods. We propose a modular computational framework that operates in the joint biomarker space, integrating preprocessing, clinical safety screening, unsupervised clustering, and centroid-based physiological interpretation. Profiles are learned exclusively from amateur soccer players during a competitive microcycle. Synthetic data augmentation evaluates robustness and scalability. Ward hierarchical clustering supports monitoring and etiological differentiation, while Gaussian Mixture Models (GMM) enable structural stability analysis in high-dimensional settings. Results. The framework identifies coherent profiles that distinguish mechanical damage from metabolic stress while preserving homeostatic states. Synthetic data augmentation demonstrates feasibility and detection of latent silent risk phenotypes typically missed by univariate monitoring. Structural analyses indicate robustness under augmentation and higher-dimensional settings. Conclusion. The framework enables interpretable identification of latent physiological states from multivariate biomarker data without injury labels. By distinguishing mechanisms and revealing silent risk patterns not captured by conventional monitoring, it provides actionable insights for individualized athlete monitoring and decision making.

Fernando Barcelos Rosito, Sebastião De Jesus Menezes, Simone Ferreira Sturza +2

1*Federal University of Health Sciences of Porto Alegre (UFCSPA), RS, Brazil. · 2Levino Inova, AC, Brazil.

Unsupervised Clustering

Mar 25, 2026cs.LG

i-IF-Learn: Iterative Feature Selection and Unsupervised Learning for High-Dimensional Complex Data

Unsupervised learning of high-dimensional data is challenging due to irrelevant or noisy features obscuring underlying structures. It's common that only a few features, called the influential features, meaningfully define the clusters. Recovering these influential features is helpful in data interpretation and clustering. We propose i-IF-Learn, an iterative unsupervised framework that jointly performs feature selection and clustering. Our core innovation is an adaptive feature selection statistic that effectively combines pseudo-label supervision with unsupervised signals, dynamically adjusting based on intermediate label reliability to mitigate error propagation common in iterative frameworks. Leveraging low-dimensional embeddings (PCA or Laplacian eigenmaps) followed by

k

-means, i-IF-Learn simultaneously outputs influential feature subset and clustering labels. Numerical experiments on gene microarray and single-cell RNA-seq datasets show that i-IF-Learn significantly surpasses classical and deep clustering baselines. Furthermore, using our selected influential features as preprocessing substantially enhances downstream deep models such as DeepCluster, UMAP, and VAE, highlighting the importance and effectiveness of targeted feature selection. Code is available at: [https://github.com/mc25800852/i_if_learn].

Chen Ma, Wanjie Wang, Shuhao Fan

SUSTech · NUS

Unsupervised Clustering Feature Selection

Feb 27, 2026cs.CC

Universal NP-Hardness of Clustering under General Utilities

Clustering is a central primitive in unsupervised learning, yet practice is dominated by heuristics whose outputs can be unstable and highly sensitive to representations, hyperparameters, and initialisation. Existing theoretical results are largely objective-specific and do not explain these behaviours at a unifying level. We formalise the common optimisation core underlying diverse clustering paradigms by defining the Universal Clustering Problem (UCP): the maximisation of a polynomial-time computable partition utility over a finite metric space. We prove the NP-hardness of UCP via two independent polynomial-time reductions from graph colouring and from exact cover by 3-sets (X3C). By mapping ten major paradigms -- including k-means, GMMs, DBSCAN, spectral clustering, and affinity propagation -- to the UCP framework, we demonstrate that each inherits this fundamental intractability. Our results provide a unified explanation for characteristic failure modes, such as local optima in alternating methods and greedy merge-order traps in hierarchical clustering. Finally, we show that clustering limitations reflect interacting computational and epistemic constraints, motivating a shift toward stability-aware objectives and interaction-driven formulations with explicit guarantees.

Angshul Majumdar

Indraprastha Institute of Information Technology, New Delhi, India

Clustering Unsupervised Clustering Combinatorial Optimization

Feb 23, 2026cs.SD

AuditoryHuM: Auditory Scene Label Generation and Clustering using Human-MLLM Collaboration

Manual annotation and clustering of audio datasets is labour intensive. We introduce AuditoryHuM, a training-free framework for the unsupervised discovery and clustering of auditory scene labels using human-Multimodal Large Language Model (MLLM) collaboration. Leveraging MLLMs, our framework generates contextually relevant labels for audio data. To ensure label quality and mitigate hallucinations, zero-shot learning (Human-CLAP) quantifies the alignment between generated text labels and raw audio. A targeted human-in-the-loop intervention, refines only the lowest aligned pairs. The discovered labels form an interpretable alignment vector to group audio into cohesive clusters. The framework was evaluated across three auditory scene datasets (ADVANCE, AHEAD-DS, and TAU 2019), achieving a 96.1% reduction in human labour for ADVANCE during testing. Downstream models trained on our clusters exhibit enhanced classification accuracy vs the baseline (0.79 to 0.84) in clean acoustic environments, though performance scales down in dense, complex soundscapes. The project page: https://github.com/Australian-Future-Hearing-Initiative

Henry Zhong, Jörg M. Buchholz, Julian Maclaren +2

Australian Hearing Hub, Macquarie University, Sydney, Australia · Google Research Australia, Sydney, Australia

Clustering LLM-Assisted Annotation Human-in-the-Loop Annotation Unsupervised Clustering Audio Understanding

Feb 20, 2026cs.AI

SOMtime the World Ain $'$ t Fair: Violating Fairness Using Self-Organizing Maps

Unsupervised representations are widely assumed to be neutral with respect to sensitive attributes when those attributes are withheld from training. We show that this assumption is false. Using SOMtime, a topology-preserving representation method based on high-capacity Self-Organizing Maps, we demonstrate that sensitive attributes such as age and income emerge as dominant latent axes in purely unsupervised embeddings, even when explicitly excluded from the input. On two large-scale real-world datasets (the World Values Survey across five countries and the Census-Income dataset), SOMtime recovers monotonic orderings aligned with withheld sensitive attributes, achieving Spearman correlations of up to 0.85, whereas PCA and UMAP typically remain below 0.23 (with a single exception reaching 0.31), and against t-SNE and autoencoders which achieve at most 0.34. Furthermore, unsupervised segmentation of SOMtime embeddings produces demographically skewed clusters, demonstrating downstream fairness risks without any supervised task. These findings establish that \textit{fairness through unawareness} fails at the representation level for ordinal sensitive attributes and that fairness auditing must extend to unsupervised components of machine learning pipelines. We have made the code available at~ https://github.com/JosephBingham/SOMtime

Joseph Bingham, Netanel Arussy, Dvir Aran

Faculty of Biology, Technion University · Taub Faculty of Computer Science, Technion University

Unsupervised Learning Algorithmic Fairness Unsupervised Clustering Unsupervised Representation Learning Self-Organizing Maps

Dec 18, 2025cs.LG

Persistent Multiscale Density-based Clustering

Clustering is a cornerstone of modern data analysis. Detecting clusters in exploratory data analyses (EDA) requires algorithms that make few assumptions about the data. Density-based clustering algorithms are particularly well-suited for EDA because they describe high-density regions, assuming only that a density exists. Applying density-based clustering algorithms in practice, however, requires selecting appropriate hyperparameters, which is difficult without prior knowledge of the data distribution. For example, DBSCAN requires selecting a density threshold, and HDBSCAN* relies on a minimum cluster size parameter. In this work, we propose Persistent Leaves Spatial Clustering for Applications with Noise (PLSCAN), a multiscale density-based clustering algorithm that replaces HDBSCAN*'s fixed minimum cluster size pruning of a mutual-reachability linkage hierarchy with a persistence-based cluster selection procedure. Effectively, PLSCAN identifies all minimum cluster sizes for which HDBSCAN* produces stable (leaf) clusters. In concept, PLSCAN applies scale-space clustering principles and is equivalent to persistent homology on a novel metric space. We compare its performance to HDBSCAN* on several real-world datasets, demonstrating that it achieves a higher median ARI, is less sensitive to changes in the number of mutual reachability neighbours, and has higher stability under resampling. Additionally, we compare PLSCAN's computational costs to

k

-Means++, demonstrating competitive run-times on low-dimensional datasets. At higher dimensions, run times scale more similarly to HDBSCAN*.

Daniël Bot, Leland McInnes, Jan Aerts

1UHasselt, Data Science Institute (DSI) · 2Tutte Institute for Mathematics and Computing · 3KU Leuven, Augmented Intelligence for Data Analytics Lab, Department of Biosystems

Clustering Unsupervised Clustering

Aug 11, 2025cs.LG

Shapley-Inspired Feature Weighting in $k$ -means with No Additional Hyperparameters

Clustering algorithms often assume all features contribute equally to the data structure, an assumption that usually fails in high-dimensional or noisy settings. Feature weighting methods can address this, but most require additional parameter tuning. We propose SHARK (Shapley Reweighted

k

-means), a feature-weighted clustering algorithm motivated by the use of Shapley values from cooperative game theory to quantify feature relevance, which requires no additional parameters beyond those in

k

-means. We prove that the

k

-means objective can be decomposed into a sum of per-feature Shapley values, providing an axiomatic foundation for unsupervised feature relevance and reducing Shapley computation from exponential to polynomial time. SHARK iteratively re-weights features by the inverse of their Shapley contribution, emphasising informative dimensions and down-weighting irrelevant ones, and is equivalent to replacing the arithmetic mean of feature dispersions with their harmonic mean. Experiments on synthetic and real-world data sets show that SHARK consistently matches or outperforms existing methods, achieving superior robustness and accuracy, particularly in scenarios where noise may be present. Software: https://github.com/rickfawley/SHARK.

Richard J. Fawley, Renato Cordeiro de Amorim

School of Computer Science and Electronic Engineering, University of Essex, Wivenhoe, UK.

Clustering Unsupervised Clustering

Jul 31, 2025stat.ML

funOCLUST: Clustering Functional Data with Outliers

Functional data present unique challenges for clustering due to their infinite-dimensional nature and potential sensitivity to outliers. An extension of the OCLUST algorithm to the functional setting is proposed to address these issues. The approach leverages the OCLUST framework, creating a robust method to cluster curves and trim outliers. The methodology is evaluated on both simulated and real-world functional datasets, demonstrating strong performance in clustering and outlier identification.

Katharine M. Clark, Paul D. McNicholas

Department of Mathematics & Statistics, Trent University, Ontario, Canada. · Department of Mathematics & Statistics, McMaster University, Ontario, Canada.

Clustering Unsupervised Clustering

Jun 6, 2025cs.LG

Scalable unsupervised feature selection via weight stability

Unsupervised feature selection is critical for improving clustering performance in high-dimensional data, where irrelevant features can obscure meaningful structure. In this work, we propose the Minkowski weighted

k

-means++, a novel initialisation strategy for the Minkowski Weighted

k

-means. Our initialisation selects centroids probabilistically using feature relevance estimates derived from the data itself. Building on this, we propose two new feature selection algorithms, FS-MWK++, which aggregates feature weights across a range of Minkowski exponents identifying stable and informative features, and SFS-MWK++, a scalable variant based on subsampling. We support our approach with a theoretical analysis, demonstrating that, under explicit assumptions on noise features and cluster structure, relevant features are assigned consistently higher weights than noise features across a range of Minkowski exponents. Our software can be found at https://github.com/xzhang4-ops1/FSMWK.

Xudong Zhang, Renato Cordeiro de Amorim

School of Computer Science and Electronic Engineering, University of Essex, Wivenhoe, UK.

Unsupervised Learning Clustering Unsupervised Clustering Feature Selection

May 23, 2025cs.LG

Unsupervised Clustering for Fault Analysis in High-Voltage Power Systems Using Voltage and Current Signals

The widespread use of sensors in modern power grids has led to the accumulation of large amounts of voltage and current waveform data, especially during fault events. However, the lack of labeled datasets poses a significant challenge for fault classification and analysis. This paper explores the application of unsupervised clustering techniques for fault diagnosis in high-voltage power systems. A dataset provided by the Réseau de Transport d'Électricité (RTE) is analyzed, with frequency domain features extracted using the Fast Fourier Transform (FFT). The K-Means algorithm is then applied to identify underlying patterns in the data, enabling automated fault categorization without the need for labeled training samples. The resulting clusters are evaluated in collaboration with power system experts to assess their alignment with real-world fault characteristics. The results demonstrate the potential of unsupervised learning for scalable and data-driven fault analysis by structuring large unlabeled waveform datasets and supporting targeted expert review.

Julian Oelhaf, Georg Kordowich, Andreas Maier +2

Pattern Recognition Lab, Friedrich-Alexander-University Erlangen-Nuremberg, Erlangen, Germany · Institute of Electrical Energy Systems, Friedrich-Alexander-University Erlangen-Nuremberg, Erlangen, Germany

Unsupervised Clustering

Jan 16, 2024stat.ML

Semidefinite programming relaxations and debiasing for MAXCUT-based clustering

In this paper, we consider the problem of partitioning a small data sample of size

n

drawn from a mixture of

2

sub-gaussian distributions in

\mathbb{R}^p

. We consider semidefinite programming relaxations of an integer quadratic program that is formulated essentially as finding the maximum cut on a graph, where edge weights in the cut represent dissimilarity scores between two nodes based on their

p

features. We define the signal-to-noise ratio (SNR) as

s^2 := \min\{n p γ^2, Δ^2\}

, where

Δ^2 := p γ

denotes the

\ell_2^2

distance between the two cluster centers. Our contributions are twofold. First, we provide a unified framework for analyzing three computationally efficient algorithms: SDP1, BalancedSDP, and Spectral clustering, yielding universal polynomial-rate misclassification guarantees for all three algorithms. Moreover, our theory allows for partial recovery (success rate

< 100\%

) as long as

s^2

is lower bounded by a constant. Second, we prove that the misclassification errors for SDP1 and BalancedSDP decay exponentially with respect to the SNR

s^2

and the BalancedSDP requires no explicit debiasing when the two clusters have equal sizes. To our knowledge, this is the first time such results are obtained for semidefinite relaxations of MAX CUT in population clustering. We provide simulation evidence illuminating the theoretical predictions.

Shuheng Zhou

University of California, Riverside, CA 92521

Semidefinite Programming Unsupervised Clustering Graph Clustering Spectral Methods

Jun 22, 2023cs.LG

Reinforcement Federated Learning Method Based on Adaptive OPTICS Clustering

Federated learning is a distributed machine learning technology, which realizes the balance between data privacy protection and data sharing computing. To protect data privacy, feder-ated learning learns shared models by locally executing distributed training on participating devices and aggregating local models into global models. There is a problem in federated learning, that is, the negative impact caused by the non-independent and identical distribu-tion of data across different user terminals. In order to alleviate this problem, this paper pro-poses a strengthened federation aggregation method based on adaptive OPTICS clustering. Specifically, this method perceives the clustering environment as a Markov decision process, and models the adjustment process of parameter search direction, so as to find the best clus-tering parameters to achieve the best federated aggregation method. The core contribution of this paper is to propose an adaptive OPTICS clustering algorithm for federated learning. The algorithm combines OPTICS clustering and adaptive learning technology, and can effective-ly deal with the problem of non-independent and identically distributed data across different user terminals. By perceiving the clustering environment as a Markov decision process, the goal is to find the best parameters of the OPTICS cluster without artificial assistance, so as to obtain the best federated aggregation method and achieve better performance. The reliability and practicability of this method have been verified on the experimental data, and its effec-tiveness and superiority have been proved.

Tianyu Zhao, Junping Du, Yingxia Shao +1

Beijing Key Laboratory of Intelligent Communication Software and Multimedia, School of Computer Science (National Pilot Software Engineering School), Beijing University of Posts and Telecommunications, Beijing, China

Federated Learning Aggregation Clustering Unsupervised Clustering Non-IID Federated Learning Clustered Federated Learning