Hierarchical Clustering

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4 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

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Latest papers 19

Oct 5, 2026cs.LG

Algorithmically Aligned Neural Agglomerative Tree Construction

Linkage algorithms for hierarchical clustering (HC) are a powerful and efficient framework for constructing clustering trees, yet it is often unclear which merge rule best suits a given dataset or task. In contrast, neural approaches can learn from data, but often fail to retain the efficiency and size generalization of classical algorithms. We introduce NN-linkage, a neural network (NN) model that can learn task-specific and locally dependent merge rules while retaining the recursive structure and efficient inference of classical linkage algorithms. In particular, our model is algorithmically aligned with the Lance-Williams (LW) recurrence, a parameterized framework for defining a broad, continuous family of linkage rules for agglomerative HC. Classical methods such as single linkage (SL), complete linkage (CL), and average linkage arise as discrete choices within this broader family. We show that NN-linkage is a universal approximator for continuous linkage functions, including LW recurrences, and, when paired with a transformer encoding, can also approximate globally dependent rules such as robust single-linkage. We further show that NN-linkage can exactly implement any symmetric constant-coefficient LW recurrence across all input sizes. On the empirical front, we evaluate NN-linkage in real-world applications, clock-tree routing and phylogenetic reconstruction, using both synthetic and real datasets, demonstrating its effectiveness over both classical algorithms and other neural approaches. By learning merge rules directly from target trees, NN-linkage extends efficient HC to scientific and engineering objectives not adequately captured by existing hand-designed linkage rules.

Robert R Nerem, Pranav Singh, Cheyenne Ward +1

University of California San Diego · University of Washington

Clustering Hierarchical Clustering Phylogenetic Inference

Oct 5, 2026cs.LG

Round-Trip KNN Clustering: multiscale hierarchical cluster detection on directed nearest-neighbour graphs

We introduce Round-Trip KNN Clustering (RTKNNC), a graph-based method for finding cluster structure at several neighbourhood scales without requiring the number of clusters in advance. Unlike approaches that first make a

k

-nearest-neighbour (KNN) graph undirected, RTKNNC keeps both directions of the neighbour relation: which points a given point selects and which points select it. Incoming selections are treated as weighted votes that help decide which local connections remain visible during a recursive forward-and-reverse traversal. Repeating the procedure for increasing

K

reveals how groups persist or merge as the neighbourhood scale grows; for the reference inverse-square model before structural refinement, clusters can merge but do not split. Because graph connectivity can occasionally join distinct groups through a sparse bridge or a small region of overlap, we add an optional label-free refinement. It first tests whether an already formed component is better described by two or three Gaussian subpopulations, and accepts a subdivision only when the proposed groups are large enough and consistent with the visible KNN graph. Across eight synthetic datasets and

K=2,\ldots,16

, independent C and Python implementations produced identical partitions in all 120 reference runs. Refinement increased adjusted Rand index from

0.7817

to

0.9627

on a variable-density benchmark and from

0.8083

to

0.9853

on a sparse-bridge benchmark. Comparisons with seven external clustering methods show competitive performance while preserving a label-free cluster-construction process.

Eraldo Pereira Marinho, Caetano Mazzoni Ranieri, Fabricio Aparecido Breve

Department of Statistics, Applied Mathematics and Computing, S˜ao Paulo State University (UNESP), Institute of Geosciences and Exact Sciences, Av. 24-A, 1515, Rio Claro, S˜ao Paulo, Brazil.

Clustering Hierarchical Clustering Graph Clustering k-Nearest Neighbors

Sep 28, 2026cs.LG

Interrelating Fruchterman-Reingold Graph Visualization and Agglomerative Clustering

Graph visualization methods and agglomerative clustering have been frequently considered in data analysis and pattern recognition. Because these approaches are interrelated and complementary, it is of particular interest to investigate their associations. In this work, we study the possible relationship between the Fruchterman-Reingold graph visualization method and four types of agglomerative clustering adopting single- and complete-linkage, average, and Ward's linkage criteria. Three types of datasets have been considered in 2 and 10 dimensions, as well as the PCA projection of the latter to two dimensions. The results obtained suggest that the relationship between the methods considered did not vary much for the three types of data mentioned above. At the same time, the agglomerative methods tended to yield results that are mostly similar to each other, while presenting moderate similarity with the original data. The Fruchterman-Reingold visualization resulted similar to the original data, but exhibited relatively smaller similarity to the agglomerative methods.

Alexandre Benatti, Luciano da F. Costa

Institute of Mathematics and Statistics - DCC University of S˜ao Paulo Rua do Mat˜ao, 1010, S˜ao Paulo, SP 05508-090 Brazil · S˜ao Carlos Institute of Physics - DFCM University of S˜ao Paulo Av. Trabalhador S˜ao-Carlense, 400, S˜ao Carlos, SP 13566-590 Brazil

Scientific Visualization Hierarchical Clustering

Sep 28, 2026eess.SP

Hierarchical Clustering and Signal Denoising on Digraphs

In this paper, we propose a representation of a digraph (directed graph) as a Hermitian matrix derived from its adjacency matrix. This representation characterizes both the connectivity and the edge orientation of the digraph. Based on the spectral decomposition of the Hermitian matrix, a digraph clustering algorithm with

k

-means is introduced to produce a partition on the graph. Applying this algorithm (bottom-up) recursively to a digraph with partially labeled vertices yields a spectral hierarchical digraph clustering (\myproj) algorithm that produces consistent nested partitions of the digraph, or equivalently, a tree structure. Furthermore, based on the in-degree and out-degree of each cluster in the digraph clustering, a pair of hierarchical interval partitions (filtrations) can be derived in a top-down manner to produce a pair of nested knot sequences. These knot sequences facilitate the construction of multilevel spline quasi-interpolants, enabling a noisy graph signal to be decomposed into a coarse approximation and inter-level details, followed by adaptive thresholding and reconstruction. Experiments on synthetic and real-world digraphs demonstrate the superiority of our {\myproj} algorithm for digraph clustering across diverse graph structural properties (homophily and heterophily) and supervision settings. Moreover, experiments on digraph signal processing using multilevel spline quasi-interpolants further demonstrate the effectiveness of signal recovery on digraphs in terms of RMSE and SNR.

Yi Wang, Sippanon Kitimoon, Hrushikesh N. Mhaskar +1

Department of Mathematics, City University of Hong Kong, Hong Kong, SAR China · Data Science Research Center, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand · Institute of Mathematical Sciences, Claremont Graduate University, Claremont, CA 91711, USA

Graph Signal Processing Hierarchical Clustering Graph Clustering Spectral Methods

Sep 22, 2026stat.ME

Automatic depth-based local center clustering via $β$ -integrated local depth and adaptive grouping

Clustering is an unsupervised learning technique that partitions unlabeled data into groups. Most existing methods require user-specified parameters, such as the number of clusters or neighborhood size. Conversely, we propose automatic depth-based local center clustering (A-DLCC), a fully data-driven method that eliminates numerical parameter tuning. A-DLCC uses the

β

-integrated local depth to identify stable exemplars, points consistently central across multiple locality levels, termed local centers, which are ranked by their representativeness. Each local center induces a group of similar points, with group-level similarity measured by a proposed nonparametric metric called group-level local similarity. To guide merging, we incorporate the bottleneck path idea from graph theory, which forms the basis of our adaptive merging criterion. Based on this criterion, we design a single agglomeration rule in which a group is either absorbed by a neighbor it reaches better than itself or bonded to a neighbor that both sides find more reachable than their own background, every merge being additionally required to be carried by a contact stronger than a configuration-model null expects. The rule automatically estimates the number of clusters and decides when to stop merging. Experiments on synthetic and real data show that A-DLCC produces interpretable clustering results without parameter tuning.

Siyi Wang, Alexandre Leblanc, Paul D. McNicholas

Clustering Hierarchical Clustering Unsupervised Clustering

Sep 11, 2026cs.LG

Hierarchical Clustering Can Jointly Satisfy Richness, Consistency, and Scale Invariance

Despite its ubiquity, clustering lacks a universally accepted definition of what is a cluster. Kleinberg's Impossibility Theorem formalizes this difficulty by showing that no flat clustering method can simultaneously satisfy three natural axioms: scale invariance, richness, and consistency. In this paper, we ask whether this impossibility persists when the output is a hierarchy rather than a single partition. We show that, in contrast to the flat clustering setting, the hierarchical analog of these axioms are jointly satisfiable. In fact, there exist uncountably many hierarchical clustering methods satisfying these axioms, which we call admissible. We explicitly construct several admissible methods, including methods based on well-separated clusters and a non-binary version of single linkage. For certain pairs of admissible methods, the hierarchy produced by one always refines that produced by the other. This refinement relation defines a partial order on the class of admissible methods. This partially ordered set has no greatest element and contains uncountably many pairwise incompatible maximal elements, revealing substantial diversity among admissible methods. Nevertheless, this diversity is constrained: every admissible method contains a hierarchy of sufficiently well-separated clusters, and every finite collection of admissible methods shares such a nontrivial common backbone.

Daichi Kuroda, Maximilien Dreveton, Matthias Grossglauser +1

School of Computer and Communication Sciences ´Ecole Polytechnique F´ed´erale de Lausanne (EPFL) Lausanne, 1015, Switzerland · LAMA, UMR-CNRS 8050, Universit´e Gustave Eiffel 5 Bd Descartes, 77454 Marne-la-Vall´ee, France

Clustering Hierarchical Clustering

Aug 7, 2026cs.LG

Density-aware Hierarchical Clustering Based on Element-Categorized Connection Subgraphs

Clustering is a fundamental data mining technique for pattern recognition through unsupervised learning. Among various clustering methods, hierarchical clustering, density-based clustering, and graph clustering stand out as representative approaches. For hierarchical clustering, it can be categorized into agglomerative and divisive modes to construct clusters in a recursive manner. The key aspect of both modes is the calculation of inter-cluster similarity, which determines whether to merge the sub-clusters into one cluster or divide a current cluster into sub-clusters. Traditionally, the similarity is derived from pairwise distances, often overlooking density variations and structural connectivity in graphs. To address this, we propose a density-aware hierarchical clustering method based on element-categorized connection subgraphs (DHC-ECS), which effectively integrates the hierarchical clustering, density-based clustering, and graph clustering. Particularly, a novel inter-cluster similarity metric is introduced that considers not only distances but also the element categorization in the KNN connection subgraphs, kernel density estimation, and local connectivity within sub-clusters. Extensive evaluations on heterogeneous benchmark datasets demonstrate that DHC-ECS exhibits superior overall performance in terms of clustering accuracy and parameter robustness compared with the baseline methods (including AChameleon, RNN-DBSCAN, McDPC, and G-RMS). The work indicates the great potential of the proposed clustering algorithm for low-dimensional datasets by leveraging local density and graph-structured connectivity (i.e., the duality of vertices and edges), as well as the possibility to determine an intrinsic threshold, reducing the reliance on manual parameter tuning.

Yuning Yu, José Rodríguez-Piñeiro, Xuefeng Yin +1

Tongji University, Shanghai, China · RadioSky (Shanghai) Communication Technology Co., Ltd, Shanghai, China

Clustering Hierarchical Clustering Graph Clustering

Jul 14, 2026cs.DS

Graph Partitioning with Demands: Generalized Conductance and its Applications

In this work, we study various graph partitioning problems under a general demand model. In each such task, we are given a graph

G=(V,E,c,w)

with a capacity function

c\colon E\to \mathbb{N}

and a demand function

w\colon V\times V\to \mathbb{N}

. Our main focus is the problem of finding a cut

(S, \bar{S})

minimizing the quantity

ψ_w( S ) = \frac{c( S, \bar{S} )}{w( S, V )\cdot w( \bar{S}, V )}.

Here,

c( S, \bar{S} )

is the cost of edges between

S

and the complement of

S

,

\bar{S}

, and

w( S, V )=w( S )+w( S, \bar{S} )

is the sum of the internal demand within

S

,

w( S )

, and the demand between vertices of

S

and

\bar{S}

,

w( S, \bar{S} )

. We call

ψ_w( S )

the \emph{generalized conductance} of the cut

(S, \bar{S})

, and the task of minimizing

ψ_w( S )

the Generalized Conductance Problem. Our main contribution is an algorithm with an

\mathcal{O}(\log n)

-approximation guarantee for this objective. Our result is achieved via a two-way reduction: first to the well-known Generalized

k

-Multicut Problem, and then to a constrained variant of the classic Sparsest-Cut Problem, with an additional upper-bound constraint on the amount of demand that may be cut. Moreover, we show that the above procedure can be used to obtain an

\mathcal{O}(\log n)

-bicriteria approximation for Graph Partitioning with Demands, where the goal is to find a minimum-cost subset of edges

C

such that for every component

H

of

G\setminus C

,

w( H )\leq ρ\cdot w( V )

. This, in turn, yields an

\mathcal{O}(\log n)

-approximation for Hierarchical Clustering with Demands, the problem of finding a hierarchy of cuts that partitions the graph into increasingly refined clusters. For multiplicative demand functions, we improve these guarantees to

\mathcal{O}(\sqrt{\log n})

and for trees we get an

\mathcal{O}(1)

-approximation for all of our objectives.

Michał Szyfelbein, Dariusz Dereniowski

Gda´nsk University of Technology

Hierarchical Clustering Approximation Algorithms

Jul 14, 2026cs.DS

Hierarchical $\mathcal{F}$ -Clustering: Approximation and Hardness of Clustering into Trees and Bounded Diameter Graphs

Consider the following variation on the Hierarchical Clustering problem: Usually, while building a hierarchical clustering, one recursively partitions the data until each cluster becomes a singleton. We relax the halting condition of the recursive process to stop whenever the remaining cluster is a graph belonging to a class

\mathcal{F}

. We call this problem Hierarchical

\mathcal{F}

-Clustering and we measure the quality of any solution using adapted Dasgupta's clustering objective. We study two natural choices of

\mathcal{F}

: trees and graphs of bounded diameter. We present the first polynomial time

\mathcal{O}(\log n\cdot\log\log n)

and

\mathcal{O}(\log n)

-approximation algorithms for clustering into trees and bounded diameter graphs respectively. Our main technical contribution is a framework for approximating such problems based on linear programming. In fact, we characterize graphs classes

\mathcal{F}

for which our approach can be applied and show that it includes both trees and bounded diameter graphs. However, our ideas are not limited to them and might be useful for other structures as well. Broadly speaking, our framework applies whenever the corresponding flat clustering problem, which we call

p_{\mathcal{F}}

-Partitioning, admits a natural ILP formulation together with a rounding procedure with provable approximation guarantees. Intuitively, given a set of vertices called terminals, the problem is to find an edge set whose removal results in satisfying certain vertex-dependent structural predicate for each terminal. We then use these ingredients to build clustering trees with the aforementioned approximation guarantees. To complement these results, we show that both Hierarchical Clustering into trees and into bounded diameter graphs cannot be approximated within any constant factor under the Small Set Expansion Hypothesis.

Michał Szyfelbein, Dariusz Dereniowski

Gda´nsk University of Technology

Hierarchical Clustering Graph Clustering Approximation Algorithms

Jul 10, 2026eess.IV

Performance Benchmarking and Optimisation of Clustering Algorithms for Local and Non-Local Similarity Measure in Medical Image Analysis

Medical imaging generates high-resolution images posing significant storage, transmission, and computational challenges. While low-rank matrix approximation (LoRMA) techniques offer efficient compression by exploiting structural redundancy, global approaches often fail to preserve local details critical for diagnosis. This paper focuses on clustering techniques that exploit non-local self-similarity to identify structurally similar regions in medical images. These clusters can be used for post-processing tasks such as adaptive image compression. We evaluate five clustering techniques: k-means, mini-batch k-means, agglomerative hierarchical clustering, balanced iterative reducing and clustering using hierarchies (BIRCH), and bisecting k-means across MRI, ultrasound, and chest X-ray modalities. All clustering techniques were optimised using random search, and cluster quality was assessed using the Silhouette score, the Davies-Bouldin (DB) index, and the Calinski-Harabasz (CH) index. Results demonstrate that standard k-means and bisecting k-means generally achieve strong cluster cohesion and separation across modalities. However, they tend to form a small number of clusters with high intra-cluster variability, limiting their effectiveness for post-processing tasks such as adaptive compression. Agglomerative clustering outperformed other techniques for MRI and ultrasound in terms of intra-cluster homogeneity, making it more suitable for preserving fine diagnostic details. For chest X-rays, mini-batch k-means achieved the best balance between clustering quality and intra-cluster compactness. BIRCH consistently underperformed across all modalities.

Sisipho Hamlomo, Marcellin Atemkeng

Department of Mathematics, Rhodes University, PO Box 94, Makhanda, 6140, South Africa · Department of Statistics, Rhodes University, PO Box 94, Makhanda, 6140, South Africa · National Institute for Theoretical and Computational Sciences (NITheCS), Stellenbosch 7600, South Africa

Medical Image Analysis Clustering Hierarchical Clustering

Jun 25, 2026cs.CL

Term-Centric Hierarchy Induction from Heterogeneous Corpora

Organizing knowledge from diverse text sources into interpretable hierarchies is crucial for tasks such as policy analysis, innovation monitoring, and exploratory domain mapping. Existing taxonomy induction methods typically rely on document-level representations that capture entire documents rather than the specific domain concepts relevant for knowledge organization, limiting their ability to generalize across heterogeneous sources. We propose a term-centric framework for inducing hierarchical taxonomies from heterogeneous corpora that scales to massive document collections. Our approach maps documents from diverse sources into a shared representation space using automatic term extraction, enabling robust cross-source alignment. Based on these representations, we construct interpretable hierarchies that integrate domain priors with datadriven clustering. Experiments on a novel English and German multi-source benchmark of over one million documents demonstrate that our method improves cross-source coherence and hierarchy quality over text- and summarybased baselines. A case study on German regional innovation analysis further demonstrates its practical utility for technology landscape mapping.

Elena Senger, Yuri Campbell, Jan-Peter Bergmann +2

1MaiNLP, Center for Information and Language Processing, LMU Munich, Germany · 2Fraunhofer Institute for Systems and Innovation Research ISI, Germany · Department of Computer Science, IT University of Copenhagen, Denmark

Clustering Hierarchical Clustering

Jun 17, 2026stat.ML

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 Programming Clustering Hierarchical Clustering Constrained Optimization

Jun 9, 2026eess.AS

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

Clustering Hierarchical Clustering Graph Clustering

Jun 1, 2026cs.LG

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

Clustering Hierarchical Clustering Semi-Supervised Learning

May 25, 2026cs.SD

Score-Agnostic Structure Analysis in Large-Scale Performance Datasets

In recent years, thanks to advances in automatic music transcription (AMT), several large-scale datasets of automatically transcribed piano solo music have been released. While these datasets undoubtedly offer extensive material for performance studies, they vary substantially in quality. In the case of classical music, performances often differ not only in expressive aspects such as tempo, but also in their structural interpretation of the score (including repeat patterns and edition-specific variants). To meaningfully use large-scale transcribed datasets for performance research, transcriptions of the same piece must be grouped according to their underlying structural realisation to support valid comparison. We address this by applying sequence-to-sequence alignment followed by hierarchical clustering: we create pairwise alignments for all pairs of transcriptions of a given piece, and use the alignment cost and (dis)similarity of performed sequence lengths to resolve structural mismatches as features for grouping. We propose this approach as a first step towards automatically evaluating large-scale transcribed datasets that lack ground-truth score and/or audio, shifting the evaluation criterion from truth-based accuracy to musical coherence and plausibility. We demonstrate our score-agnostic approach on around 1,500 transcriptions of 88 compositions from a recently published large-scale transcribed piano performance dataset.

Patricia Hu, Silvan Peter, Gerhard Widmer

Institute of Computational Perception, Johannes Kepler University, Linz, Austria · LIT AI Lab, Linz Institute of Technology, Linz, Austria

Hierarchical Clustering Music Information Retrieval Sequence Alignment

May 20, 2026cs.LG

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 Recognition Clustering Hierarchical Clustering Gesture Recognition

May 8, 2026stat.ML

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

\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(\varepsilon^{-γ})

and depth

\widetilde O(\varepsilon^{-3γ/2})

, where

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 Classification Clustering Hierarchical Clustering Hierarchical Representation Learning

Apr 26, 2026cs.DS

Characterizing Admissible Objective Functions for Hierarchical Clustering

Hierarchical clustering is a fundamental task in data analysis, but classical methods have long lacked a principled objective function. Dasgupta [STOC 2016] took an important step toward addressing this gap by proposing a well-motivated objective function for cluster trees. Cohen-Addad et al. [J. ACM 2019] subsequently introduced the notion of admissibility: an objective function is admissible if, whenever the input similarity matrix admits generating trees, its minimizers are precisely those generating trees. They also gave a necessary and sufficient condition for admissibility within a family of objective functions based on aggregate intercluster similarity. We refer to this family as sum-type objective functions. However, apart from Dasgupta's original objective function, no explicit admissible objective functions in this family were provided. In this paper, we study admissible objective functions for hierarchical clustering in two directions. For sum-type objective functions, we give a complete characterization when the scaling function is a symmetric polynomial of degree at most two, and we derive sufficient conditions for degree-three polynomials. We also show that the recursive sparsest cut algorithm achieves an O

(φ)

-approximation ratio for the admissible objective functions covered by our characterization, where

φ

is the approximation factor of the sparsest cut subroutine. We then introduce max-type objective functions, where cluster interaction is measured by maximum, rather than aggregate, intercluster similarity. For this class, we characterize which objective functions are admissible for arbitrary symmetric scaling functions and give a complete characterization when the scaling function is a symmetric polynomial of degree at most two.

Ryuki Tsukuba, Kazutoshi Ando

Graduate School of Integrated Science and Technology, Shizuoka University,Jun Hamamatsu, Shizuoka 432-8561, Japan · Faculty of Engineering, Shizuoka University, Johoku 3-5-1, 432-8561 Hamamatsu, Japan

Clustering Hierarchical Clustering

Apr 25, 2026eess.AS

Explainable AI in Speaker Recognition -- Making Latent Representations Understandable

Neural networks can be trained to learn task-relevant representations from data. Understanding how these networks make decisions falls within the Explainable AI (XAI) domain. This paper proposes to study an XAI topic: analysing, visualising and understanding the unknown organisation of network representations, particularly those a speaker recognition network learns from utterances, for recognising speaker identity. Past studies have employed algorithms (e.g. K-means) to analyse the different ways in which network representations can be naturally grouped into clusters, i.e. to analyse different flat clustering phenomena within the space defined by those representations. In contrast, this work applies two algorithms -- Single-Linkage Clustering (SLINK) and Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) -- to analyse the different ways in which representations from the speaker recognition network can form clusters with hierarchical relationships, i.e., to analyse different hierarchical clustering phenomena within the representation space of the speaker recognition network. Furthermore, an algorithm called Hierarchical Cluster-Class Matching (HCCM) is designed to semantically interpret one of the above hierarchical clustering phenomena analysed using SLINK. Given the clusters representing this phenomenon, HCCM identifies which ones best match individual semantic classes related to gender and nationality (e.g.\ male, female, Ireland, UK) and and-logic conjunctions of these classes (e.g.\ female and Ireland). The Liebig score metric is also proposed within HCCM to quantify the matching quality of each cluster-class pair and diagnose the factor that limits each match.

Yanze Xu, Wenwu Wang, Mark D. Plumbley

Centre for Vision, Speech and Signal Processing, University of Surrey, Guildford, GU2 7XH, UK · Department of Informatics, King’s College London, London, WC2R 2LS, UK

Clustering Hierarchical Clustering Speech Processing Neural Network Interpretability