Image Clustering

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.

We introduce Graph Neural Automata Clustering (G-NAC), an unsupervised clustering method in which observations interact as cells on a fixed neighborhood graph. A shared recurrent graph-neural cellular rule evolves latent domain states through local interactions, which are converted into a rank-based spectral affinity for partitioning. Across 73 clustering tasks from 57 benchmark datasets, G-NAC achieved a mean adjusted Rand index (ARI) of 0.7951, comparable to Genie at 0.7941 and higher than the other evaluated baselines. Empirical training time and GPU memory scaled approximately linearly from 5,000 to 100,000 nodes. Learned transition rules also transferred from smaller source graphs to independent 100,000-node samples generated under matched conditions. These results demonstrate a recurrent graph-clustering formulation while identifying dependencies on graph quality, readout design, and source-target similarity.

Spectral co-clustering is a useful tool for discovering latent structure in word-document matrices, but its reliance on singular value decomposition (SVD) can make standard formulations expensive on high-dimensional data. This paper presents two randomized approximations for normalized spectral co-clustering of bipartite text data when the numbers of document and word clusters may differ. The first method uses randomized SVD through random projection, while the second combines partial SVD with element-wise random sampling. Across real-world and synthetic datasets, both methods reduce runtime relative to the full-SVD baseline, but their behavior depends on matrix sparsity. The random projection method is the more reliable approximation across the tested settings, whereas the sampling-based method is most useful on denser matrices and provides limited benefit on already sparse text data. These results show that randomized approximations for spectral co-clustering should be selected according to the underlying structure of the data.

We study federated soft clustering over federated learning (FL) networks of devices that each hold a private local dataset and fit a personalized Gaussian mixture model (GMM). Generalized total variation minimization (GTVMin) couples the local maximum likelihood problems through a graph regularizer that penalizes a discrepancy between the models of connected nodes. The choice of discrepancy measure is a key design decision: we compare a squared Euclidean distance between model parameters, which requires component matching, with two measures that compare the local model distributions directly and hence need no matching: a Monte-Carlo approximated Kullback-Leibler (KL) divergence and a closed-form maximum mean discrepancy (MMD). All three resulting GTVMin instances are optimized by synchronous projected gradient updates; for the smooth MMD instance we provide a convergence guarantee to stationary points. We characterize their computational cost and evaluate their robustness to data heterogeneity.

Diagnostic errors and mislabeling are common in biomedicine, which compromise the reliability of predictive models and data-driven outcomes. Stratifying unlabeled biomedical data based on complex relationships between features eliminates the need for data labels and overcomes the limitations of supervised learning. Traditional clustering methods assume restrictive data distributions, making them suboptimal for capturing complex dependencies in high-dimensional biomedical data. This paper introduces a novel cluster-friendly data presentation framework that integrates the non-Gaussian and non-linear feature dependence of copula models with an ensemble of causal structure discovery (CSD) methods based on Directed Acyclic Graphs (DAGs). While copulas model flexible multivariate distributions by relaxing assumptions related to multivariate normality, linear dependence, and symmetric relationships, an ensemble of DAG-based CSD methods identifies stable causal relationships between features. When clustered using K-means, the new data representation obtained by the proposed copula-adapted DAG (CopDAG) ranks first among the 12 methods in normalized clustering accuracy and adjusted Rand index across 16 biomedical datasets. Our CopDAG method predicts ground-truth class labels directly from feature relationships without data annotations and supervised learning, while also providing cluster visualizations and explainable causal structures of the biomedical data features.

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.

Accurate plant growth estimation is essential for greenhouse monitoring, yet obtaining labeled data remains costly and time-consuming. To address this, we propose a few-shot regression framework that combines Vision Transformer (ViT) feature embeddings, clustering-based task construction, and gradient-based meta-learning, and show that task construction in embedding space is a primary driver of performance. The approach leverages an unlabeled image pool to organize data into structured tasks using fuzzy c-means clustering, enabling efficient learning from a small number of labeled samples. We systematically evaluate meta-learning methods and show that second-order methods (e.g., Model-Agnostic Meta-Learning variants such as MAML++) outperform classical baselines in the few-shot regime. Furthermore, intra-cluster support selection has a limited and dataset-dependent impact. Experiments on two plant datasets show that structured task design combined with meta-learning enables reliable plant growth estimation under severe label scarcity.

The success of generative retrieval has largely been attributed to the use of Semantic IDs, which improve over arbitrary item-level identifiers such as hashes by capturing the semantics of items. The main challenges faced when constructing Semantic IDs, however, is in mapping each identifier to a unique product and capturing information valuable to downstream tasks. Past works have appended additional codewords to de-duplicate item identifiers and utilized residual quantization to create hierarchical clusters. In this work, we present an algorithm for generating Semantic IDs that ensure the identifiers are both unique and preserve the structure of the original embedding. Key to our work is the use of bottom-up clustering to preserve local structure in the embedding space, improving the clustering quality of the resulting Semantic IDs and their utility for downstream generative retrieval.

Fairness in clustering has attracted sustained research interest, motivated by the need to ensure equitable representation of protected groups in machine learning applications. We study fair $k$-means clustering in Euclidean space, where the proportion of each protected group in every cluster must lie within specified lower and upper bounds. These constraints make it challenging to determine both cluster centers and point assignments. We propose an approximation algorithm that combines a linear programming relaxation with geometric transformations of the input to construct candidate center sets. Given a $ρ$-approximate algorithm for weighted $k$-means and any $ε>0$, our algorithm returns a fractional solution whose cost is at most $1+(3-1/Γ)ρ+O(ε)$ times the optimal integral fair cost, where $Γ\approx6.357$ is an upper bound on the integrality gap of the standard Euclidean $k$-means LP. With a PTAS as the subroutine, the approximation ratio becomes $3.8427+O(ε)$, improving the previous factor of $5+O(ε)$ to below $4$. The solution satisfies all fairness constraints exactly and can be rounded to an integral assignment with a bounded additive violation of fairness and no increase in cost. The same approximation guarantee extends to the $k$-sparse Wasserstein barycenter problem.

Time series data is very common in many real-world applications and in numerous domains, with increasing interest for automated information extraction using machine learning. One of these subfields is time series clustering, which consists in identifying clusters among a set of time series in an unsupervised fashion. Most time series clustering algorithms suffer from the same balancing act: they trade clustering performance for faster runtimes or vice versa. We present a novel time series clustering algorithm that we call CLUES-WEASEL, which stands for CLustering with the UnsupervisEd Second version of Word ExtrAction for time SEries cLassification. CLUES-WEASEL extracts features using the unsupervised version of the transformation step of WEASEL 2.0, which is a time series classification algorithm, then reduces these features using principal component analysis, and finally performs clustering with the $k$-means algorithm using these reduced extracted features. Through extensive experiments, we prove that CLUES-WEASEL is significantly better than any other existing time series clustering algorithm while being (much) faster than any state-of-the-art one. We also show that the architecture of CLUES-WEASEL can work well with other time series feature extraction algorithms. Our findings highlight the relevance of CLUES-WEASEL for time series clustering.

Existing graph-clustering methods typically improve clustering performance by optimizing model parameters and node representations. Effective means of further improving the clustering results of an already trained and frozen model, however, remain limited. We study post-processing for frozen graph clustering. After checkpoint fixation, the procedure uses no labels and updates neither model parameters, node representations, nor the original graph structure. Instead, it exploits an attribute hypergraph to supplement higher-order relations that ordinary graphs cannot readily express, thereby refining existing cluster assignments. Because global hypergraph refinement can yield both performance gains and erroneous updates, we propose Selective Hypergraph Refinement (SHR). The method generates candidate residual directions from the hypergraph and evaluates their reliability using graph structure, node attributes, and matched-null evidence. It updates only nodes with sufficient support and otherwise retains their original assignments. Further analysis shows that whether a node changes cluster is jointly governed by its native assignment gap and the directional strength of the refinement. In a controlled common-suite evaluation, 13 of 15 backbone-dataset cells had a positive mean macro gain, one produced exact no-action, and one was negative. The cell-equal macro gain was 0.066 pp (95% bootstrap CI, [0.030, 0.107] pp), while only 0.209% of hard assignments changed on average. A broader 15-combination native-interface evaluation yielded a macro gain of 0.137 pp at a mean change ratio of 0.375%. These results indicate that frozen clustering outputs retain a limited but measurable refinement space after training. The effect is heterogeneous across backbone-dataset pairs, and broader coverage also increases exposure to negative transfer.

This paper introduces the Sierpiński-Knopp (SK) Wasserstein distance, a fast metric between persistence diagrams. The SK-Wasserstein distance, denoted $d_{\mathrm{SK}}$, maps diagram points and their diagonal projections to the unit interval via the Sierpiński-Knopp space-filling curve on the upper diagonal triangle. The encoded point sets are then efficiently matched via one-dimensional optimal assignment, in $O(N\log N)$ steps, yielding an explicit diagonal-aware point assignment between the two input persistence diagrams. We show that the SK-Wasserstein distance controls the classical $2$-Wasserstein distance between diagrams, admits an explicit isometric embedding into a Hilbert space, and induces a positive-definite Gaussian kernel, making the resulting geometry directly compatible with Euclidean and kernel-based learning methods. A tighter surrogate dissimilarity, noted $W_Γ$, is also introduced based on the point assignments along the curve. Experiments on 12 scientific collections comprising 227 diagrams show median per-collection speedup of $d_{\mathrm{SK}}$ over state-of-the-art approximations of $W_2$ is $626\times$, while the aggregate speedup over the full benchmark is $2100\times$. Average-linkage partitions obtained from $d_{\mathrm{SK}}$ and $W_Γ$ each exactly match the corresponding $W_2$ partition on 8 of the 12 collections. Hilbert $k$-means and Gaussian spectral clustering, both based on $d_{\mathrm{SK}}$, achieve mean adjusted Rand indices (ARI) of $0.756$ and $0.800$, respectively, with respect to the benchmark reference partitions, compared to $0.750$ obtained by average linkage on $W_2$. The Gaussian $d_{\mathrm{SK}}$ kernel supports other kernel-based analysis tasks, as illustrated by its use for contiguous segmentation of ordered diagram collections in our experiments.

Multiple kernel $k$-means integrates complementary nonlinear similarities by learning a combination of base kernels. Its pointwise optimization, however, is sensitive to noisy and boundary samples and repeatedly operates on sample-scale kernel matrices. Granular-ball representations organize local sample groups into mesoscopic units, but granular balls generated once in the input space may be inconsistent with the fused-kernel geometry that evolves during multiple kernel learning. We propose dynamic kernel-space granular-ball multiple kernel $k$-means (DK-GBMKKM). The method generates granular balls in the current fused kernel space and alternates kernel-weight learning with granular-ball membership updates, allowing the representation to adapt to changes in the fused-kernel geometry. A sample-size-weighted granular-ball kernel is further constructed to preserve the contributions of balls of different sizes, and its positive semidefiniteness and related equivalence properties are established. Experiments on 12 public datasets demonstrate the strong overall clustering performance of DK-GBMKKM. The code has been open-sourced for reproducibility: https://github.com/lianxiaoyu724/DK-GBMKKM.

This paper studies the problem of computing the stochastic probability (shortest code length) of the encoded vectors containing cluster structure using Normalized Maximum Likelihood (NML) model. This is of great theoretical and practical importance in data clustering based on Minimum Description Length (MDL) principle, such as for estimating the best number of clusters and best cluster structure for the data. Straightforward computation of the shortest code length of the vector containing cluster structure based on the NML model requires polynomial time with respect to the size of the vector and number of clusters. We show that this is a tractable problem by introducing a recursion formula for the efficient computation of normalizing constant from the NML model. The time complexity of the new formula is linear opposed to previous polynomial time with respect to the size of the vector and number of clusters.

Semantic identifiers (SIDs) represent entities as hierarchical token sequences for generative retrieval and recommendation. Residual-quantization tokenizers construct these sequences by selecting a codeword at each level and passing a residual to the next. We view this process as progressive commonality removal: each token captures a component shared within its group, while later tokens should model the remaining differences. This view reveals three limitations: a corpus-wide shared component can consume first-level capacity, hard assignment ignores graded similarities to nearby codewords, and full-codeword subtraction can leave variation along the selected-codeword direction in the next residual. We therefore develop our solution in the post-hoc setting, where residual construction is not constrained by input reconstruction. Specifically, we propose PRQ-KMeans, which removes the global-mean component, refines centroids with Top-k similarity-weighted updates, and replaces full-codeword subtraction with a projection residual that removes each representation's selected-centroid component. Experiments on a large-scale industrial search dataset and four public recommendation benchmarks show that PRQ-KMeans achieves the strongest overall performance among the evaluated tokenizers, including gains of up to 7.4% in HitRate and 11.8% in MRR on the industrial dataset.

Classification of edible oils in processed foods is important for food quality, fraud prevention, and regulatory compliance. This study develops a Mutually Exclusive, Collectively Exhaustive framework integrating spectral organization, interpretable classification, Physics-Informed Artificial Intelligence (PI-AI), and Frugal AI-based feature reduction. Five edible oils were analyzed in pure form and within a fried-potato-chip matrix using t-SNE, K-means clustering, Decision Trees, and Non-Negative Least Squares (NNLS)-based spectral decomposition. Unsupervised analyses showed stronger class organization and separability in pure oils, while food-matrix effects caused substantial spectral overlap. Decision Trees achieved 100% classification accuracy for pure oils using only four Raman variables from 1866 spectral features. These variables represented only 0.21% of the available spectral information while retaining perfect test-set performance. Two variables associated with lipid unsaturation (about 1650 cm-1) and hydrocarbon-chain organization (about 1127 cm-1) remained important after NNLS matrix correction. Their combined contribution increased from 50% in pure oils to about 62% and 89% in paper-subtracted and paper-plus-potato-subtracted datasets, respectively. NNLS-based PI-AI improved food-matrix classification by separating oil signatures from paper and potato contributions. Optimized post-pruned models achieved nearly 80% test accuracy using only five and four Raman variables, respectively. The four-feature representation reduced the data footprint by 99.44% without loss of accuracy. These findings demonstrate that Raman-based oil identification can use compact, physically meaningful, and interpretable spectral representations, supporting Frugal AI, Edge AI, portable sensing, and embedded food-quality monitoring.

The study presents a systematic machine learning (ML) study of 6G-IoT beamforming optimization (6GBO) using supervised and unsupervised approaches. We compared the predictive power of network, environmental, device, and vision feature groups for 6GBO. Additionally, it addressed other unsupervised perspectives that can enhance 6GBO, including clustering network scenarios using methods such as K-means, DBSCAN, and hierarchical clustering. Several imbalance-aware experiments revealed that network features possess better prediction power than device, environmental, and vision feature groups, as evidenced by their recall, F1-score and ROC-AUC values. For unsupervised ML exploration (assessed using Elbow, Silhouette score, and Davies-Bouldin Index methods), the results indicate that the deployment environment and type of device primarily influence clustering, rather than mobility-based attributes. Furthermore, the explainability analysis showed that bandwidth, IoT sensors, and mobility possess higher global feature importance across the feature groups. In the future, we would apply deep and reinforcement learning techniques to predict throughput/latency or to optimize rewards determined by performance indicators like SNR enhancement

Clustering is a fundamental class of data analysis techniques with the most important representatives being centroid-based methods like $k$-means. Such methods are strongly connected to quantization problems, which aim to approximate general probability measures with discrete ones. For example, $k$-means corresponds to quantization with respect to the Wasserstein distance. While Wasserstein quantization clusters points within a fixed space, this paper studies Gromov-Wasserstein (GW) quantization, which additionally aims at clustering the ambient geometry of the space. We show existence of solutions to the GW quantization problem and give a characterization that justifies an analogue to the $k$-means algorithm (Lloyd's algorithm) to approximate them numerically. We further calculate the quantization rate for usual Euclidean geometries that are used in the GW context, and relate it to standard Wasserstein quantization rates. Finally, numerical experiments show that GW quantization opens up many modeling possibilities beyond normal clustering methods (e.g., for geodesic distances of 3D shapes or structured pruning of neural networks) and that the introduced algorithm leads to useful numerical solutions with approximation quality often in line with theoretically optimal rates.

Spectral clustering methods for network data are commonly based on a few matrix representations, such as the adjacency matrix and the symmetric Laplacian. We study a continuum of degree-normalized spectral embeddings that includes these commonly used choices as special cases. Under a random dot product graph model, we establish a row-wise central limit theorem for this family of embeddings. The result provides an explicit description of how degree normalization affects both population geometry and the local uncertainty of embedded nodes. We use the limiting distributions to compare different normalizations in two-community stochastic block models through a projected-Gaussian Bayes-error diagnostic. These comparisons show that no single normalization is uniformly preferred. Instead, the favored normalization depends on network density, community imbalance, and block-probability structure. Typically, stronger normalization is favored in lower-density or more imbalanced settings. These results provide a unified distributional understanding of when and why alternative normalizations may improve spectral clustering.

Long speech separation typically employs a segment-separation-stitch paradigm where recordings are divided into short segments, processed independently, and stitched together. Its challenge lies in predicting cross-segment permutations. This paper proposes a training-free dynamic clustering approach for cross-segment permutation alignment using speaker embedding reference pools. The method predicts the permutation using the cosine similarity between current segment embeddings and the reference pools. The approach updates reference pools by retaining the most representative speaker embeddings based on their overall cosine similarity with existing references. As a plug-and-play post-processing module compatible with existing separation models, the proposed method demonstrates superior performance compared to existing methods on dense and sparse long speech scenarios, particularly in challenging sparse scenarios with extended utterance gaps, and further shows robustness to speaker count estimation errors in unknown speaker count scenarios.

Leveraging textual information for image clustering has emerged as a promising direction, largely owing to the powerful representations learned by Vision-Language Models (VLMs). Existing approaches typically retrieve a textual counterpart for each image and then refine multimodal representations by directly enforcing cross-modal agreement, e.g., maximizing image-text similarity inherited from pretrained VLMs. However, such a strategy aligns heterogeneous representations across modalities without explicitly modeling the intrinsic structure within each modality and thus might yield unreliable alignment or distort modality-specific structures that are crucial for clustering. In this paper, we propose a simple but principled approach, termed deep modality-shared self-expressive model (DeepMORSE), which discovers cross-modal structures via a modality-shared self-expressive model and simultaneously learns structured representations that conform to a union of modality-specific subspaces. Moreover, we theoretically justify that the modality-shared self-expressive coefficients suppress inter-class noise towards a subspace-preserving solution, and show that mini-batch optimization procedure introduces an implicit regularization onto the self-expressive model. We evaluate our DeepMORSE on six widely used image clustering benchmarks and observe performance improvements exceeding 3% on the UCF-101, DTD-47, and ImageNet-Dogs datasets. In addition, we demonstrate the strong transferability of the learned representations by achieving state-of-the-art performance on downstream tasks such as image retrieval and zero-shot classification---without requiring any task-specific losses or post-processing. The code is available at: https://github.com/mengxianghan123/DeepMORSE.

Clustering mixed tabular data requires a unified metric space to bridge the inherent heterogeneity between continuous numerical measurements and discrete categorical symbols. Traditionally, algorithms rely entirely on dataset-internal statistics to estimate categorical relationships, which confines the learned metric to empirical co-occurrences and ignores conceptually obvious yet statistically unobserved affinities. Although LLMs offer external world knowledge, applying their text-centric reasoning to highly abstract tabular concepts presents significant challenges. Bridging this modality gap to construct a semantically complete metric typically requires embedding LLMs into iterative metric learning loops to dynamically optimize cross-modality representations. This incurs intractable computational overhead, forcing a compromise between semantic enrichment and scalability. Therefore, we propose GRACE, an LLM-grounded framework for scalable mixed-data clustering. GRACE shifts semantic acquisition to the attribute-value level via a multi-perspective LLM querying strategy, mapping heterogeneous values into knowledge-informed descriptions. Crucially, this one-shot grounding extracts general-purpose semantic representations that embed heterogeneous attributes into a unified space, decoupling expensive LLM invocation from iterative optimization. Furthermore, GRACE cross-validates these external semantics against dataset-internal statistical evidence to ensure alignment with the dataset-specific cluster structure. Ultimately, GRACE matches the scalability of conventional statistics-driven baselines while achieving superior clustering accuracy and conceptual interpretability over 11 competing methods. The source code is available at https://github.com/develop-yang/GRACE-GRACE-A

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.

Deep Belief Networks (DBNs) learn hierarchical generative models without class supervision. Here, we ask whether this purely unsupervised process nevertheless organizes internal representations according to the unknown data classes. We analyze successive layers of DBNs trained on MNIST, Fashion-MNIST, and KMNIST using the Generalized Discrimination Value (GDV), supervised probes applied only after training, a reconstruction-based measure of abstraction distance, effective dimensionality, and free sample generation. Remarkably, class-specific clustering generally increases with depth across datasets and network widths, although no label information is available during DBN training. Control experiments show that this effect depends on the learned feature structure and cannot be explained by random transformations, weight marginals, dimensionality reduction, or sigmoid saturation. The first hidden layers also frequently make class identity more accessible to linear and nonlinear probes. With greater depth, representations become increasingly compact and prototype-like as neurons acquire correlated feature directions. At the same time, GDV and probe accuracy reveal complementary aspects of class structure: improved average clustering can coexist with reduced accessibility for a few difficult class pairs. These findings demonstrate that layer-wise generative learning can spontaneously uncover and progressively amplify class-related structure in unlabeled data.

Interpreting clustering outcomes remains a fundamental challenge in data analysis, particularly in domains such as healthcare where meaningful patterns must be extracted from high-dimensional data. While numerous explainability techniques exist, they are primarily designed to assess feature importance or provide local instance-level explanations rather than to identify structured patterns present within clusters. This work presents a comparative evaluation of commonly used post-hoc analysis methods for pattern detection in clustering results. To enable controlled evaluation, we introduce a suite of synthetic datasets in which predefined patterns are systematically injected. Three widely used techniques are evaluated: a Random Forest surrogate model with permutation feature importance, LIME (Local Interpretable Model-agnostic Explanations), and principal component analysis. Results demonstrate that although each method can successfully recover relevant features, none consistently detects all injected pattern types. These findings high- light a critical gap between existing explainability tools and the requirements of pattern-level cluster interpretation, motivating the development of dedicated pattern detection methodologies.

This work focuses on the problem of learning on temporal graphs, with particular emphasis on the task of clustering: obtaining coarse-grained representations by aggregating information from nodes, edges, and temporal dynamics - a task related to pooling in machine learning on graphs, or community detection in network science. Although graph neural networks reach state-of-the-art performance across many downstream graph tasks, their advantage over established descriptive and inferential clustering algorithms is far less settled, especially under demands of efficiency and recovery accuracy. We frame this tension through three linked perspectives: principles, connecting graph learning and community detection through shared spectral foundations and detectability thresholds in stochastic block model regimes; primitives, making spectral clustering and multislice modularity optimization tractable through GPU-accelerated temporal backends; and pooling, viewing principled community detection as a theory-grounded coarse-graining operator for temporal graphs. Our results indicate that algorithmic methods remain the appropriate tool where attributes are absent or weak - scalability rather than accuracy being the binding obstacle - while neural models are most compelling when structural, temporal, and attribute signals align. By making temporal clustering scalable, GPU-accelerated primitives suggest a route toward theory-grounded pooling, while raising a central question: when does community-based coarse-graining preserve the dynamics needed for downstream learning tasks?

Large Language Model-assisted Evolutionary Search (LES) has emerged as a powerful paradigm for automated algorithm design. However, existing LES methods primarily optimize for average performance, inherently directing search effort toward instances that contribute most to this metric while leaving others poorly served, resulting in weak tail robustness and limited real-world reliability. To address this limitation, we propose Dynamic Instance Clustering and Specialized Algorithm Design (DyCA), an LES framework with a feature-free, structure-aware mechanism for constructing reliable algorithm portfolios under heterogeneous instance distributions. DyCA treats instance clustering as a co-evolving component within the search process, reusing accumulated evaluation data as feature-free signals to progressively partition instances with similar algorithmic response patterns. The uncovered clusters decompose the mixed objective into a set of structure-aware sub-objectives, thereby enabling finer-grained and more adaptive guidance for specialized algorithm design. Experimental results across four algorithm design tasks with heterogeneous instances demonstrate that DyCA outperforms state-of-the-art LES baselines, improving tail robustness by an average of 15.2% and overall performance by 7.1% while maintaining competitive head performance.

Malware clustering is a critical task in cybersecurity that helps discover threats and analyze evolving malware families. While self-supervised learning (SSL) and tabular representation learning (TRL) have achieved breakthroughs in other domains, their application to binary program clustering (the task of clustering all incoming samples regardless of label) remains largely unexplored. This study presents the first systematic investigation of SSL and TRL methods for binary program clustering, conducted in two phases on the public Ember and Bodmas datasets. In Phase 1, we establish a performance ceiling by adapting prominent vision-based SSL models (BYOL, SimSiam, Barlow Twins, VICReg) for tabular data with supervised pair generation, finding that BYOL and SimSiam achieve performance comparable to fully supervised models, while Barlow Twins and VICReg significantly underperform. In Phase 2, we evaluate purely unsupervised TRL methods against strong baselines (PCA, Autoencoder, UMAP), demonstrating that VIME establishes a new state of the art for binary program clustering. Informed by these findings, we propose VIME-R, a retrieval-augmented extension of VIME that replaces random marginal-distribution corruption with retrieval-based augmentation to generate more informative training pairs. VIME-R further improves upon VIME, achieving 2.7%-5.8% higher Homogeneity on both datasets. Our results highlight retrieval-augmented tabular representation learning as a promising direction for enhancing automated malware analysis. Code will be made available.

Data imbalance poses a major challenge in supervised classification, where the majority-class bias contributes to false negatives and overestimates classification accuracy. Unsupervised deep clustering can be immune to class imbalance because representation learning for clustering is performed without class labels. Deep clustering has been proposed for images, languages, and graphs, while its application to tabular data has only emerged recently. This paper is among the first to examine the performance of state-of-the-art deep clustering methods under varying levels of data imbalance. We introduce two novel cluster ensemble approaches: one aggregates deep clustering assignments across different embedding dimensions, and the other applies majority voting to the best-performing clustering algorithms. Experiments on 16 binary tabular datasets with varying and artificially induced levels of imbalance reveal distinct strengths of different deep clustering methods. On average, our ensemble methods outperform individual clustering methods in ACC, NMI, and ARI scores, offering greater resilience to data imbalance when identifying ground-truth classes without supervision. Therefore, in an imbalanced data scenario, deep clustering can serve as a strong alternative to supervised classification.

Clustered Federated Learning (CFL) addresses data heterogeneity in federated settings by grouping clients with similar data distributions to enable effective training. Existing methods face a trade-off between privacy preservation, communication cost, and computational efficiency. We formalize this as the CFL trilemma, according to which improving two of these dimensions comes at the expense of the third. A prominent paradigm relies on metadata (i.e., low-dimensional representations of client datasets shared with the server) to enable communication- and computation-efficient clustering. However, such approaches are not compatible with standard FL privacy-preserving mechanisms. To address this limitation, we propose FLAMECHE, which reformulates metadata-based CFL as a distributed Expectation-Maximization (EM) procedure, restricting server updates to additive operations while preserving efficiency. This design enables compatibility with practical secure FL schemes. We conducted extensive experiments on multiple datasets under various heterogeneous scenarios. Results show that FLAMECHE improves the effectiveness of client models. It enables encryption-compatible metadata-based clustering, enhancing its positioning within the CFL trilemma.

Mapping an atomic structure to a compact set of geometric descriptors is an essential step in any machine-learning application to atomic-scale modeling. A powerful and widely-used approach can be understood as a discretization of the histogram of pair distances, triangles, etc., that results in a hierarchy of symmetry-invariant atom-centered descriptors. Unfortunately, the lower rungs on this hierarchy (two, three, four-neighbor clusters) were found to be incomplete, with symmetry-unrelated pairs of structures having exactly the same descriptors. However, all the ``descriptor degeneracies'' reported so far are resolved by considering larger clusters of neighbors to build the descriptors. We report examples of 3D structures that are indistinguishable even if one considers clusters of up to seven neighbors, and to arbitrary order when considering a practical level of discretization of the descriptors, discovered with the assistance of large language models. The key ingredients in their construction can be traced to results that have been known for decades in different communities; the model was able to find the references and recognize their significance for the problem at hand. We believe this experiment exposes an extremely fruitful usage pattern for AI in science: translating results between different communities and application domains, accelerating the process by which serendipitous discoveries in a field become paradigm-shifting breakthroughs in another.

The $k$-means++ algorithm is a standard and widely used seeding method for $k$-means clustering, but for a fixed number $k$ of centers its worst-case expected approximation ratio is $Θ(\log k)$. We consider the same algorithm when an adversary first fixes the dataset and some $K$; the number of centers $k$ is then chosen uniformly from $\{K,\ldots,2K-1\}$. We prove that $k$-means++ is an $O(1)$-approximation with constant probability in this budget-smoothed setup.

Single-cell ribonucleic acid sequencing (scRNA-seq) is a foundational technology for precision-medicine workflows that contribute to United Nations Sustainable Development Goal 3 on Good Health and Well-being, and unsupervised clustering is the analytical step that turns raw expression matrices into interpretable cell populations. Practitioners therefore face a recurring engineering decision: is an additional deep representation stage worth its compute and tuning cost, or do classical principal component analysis (PCA) pipelines already suffice? We address this question with a diagnostic benchmark of nine clustering pipelines on ten real datasets (90-5,685 cells, 19,046-41,480 genes, 4-11 cell types), augmented by a partial scVI V2 specialized comparison on seven datasets. The protocol integrates Optuna hyperparameter search, repeated-run robustness, Friedman/Wilcoxon-Holm/TOST testing, and Sobol total-order sensitivity analysis. The contrastive autoencoder achieved the highest mean Adjusted Rand Index (0.7872), but Holm-corrected tests did not establish dominance over the strongest baselines. Per-dataset analysis reveals three reproducible regimes: probabilistic variational autoencoder (VAE) variants help on the smallest datasets, deep autoencoders win on mid-scale data with multi-batch or many-type structure, and classical PCA pipelines remain competitive when linear projection already captures the dominant variation. Sobol indices identify learning rate ($S_T=0.70$) and latent dimensionality ($S_T=0.56$) as the dominant variance contributors, indicating where limited tuning budgets should be allocated. The contribution is therefore a dataset-aware and compute-conscious decision framework for biomedical AI pipelines supporting sustainable healthcare analytics, rather than a universal superiority claim.

Lloyd's $K$-means algorithm, also known as naïve $K$-means, is a widely used ad hoc optimization heuristic, designed to minimize the sum of squared errors (SSE) across all $K$-partitions of a dataset via iterative cluster refinement. In this work, we establish a novel connection between Lloyd's algorithm and the Frank-Wolfe (FW) algorithm, a prominent first-order method for projection-free optimization. We demonstrate that Lloyd's algorithm is a special case of FW. Leveraging recent advances in FW methods for concave objectives, we derive a non-asymptotic $\mathcal{O}(1/t)$ convergence rate to a local minimum of the SSE objective. To account for empty clusters, an outcome possible under Lloyd's greedy assignment, we develop an FW variant for semismooth objectives while retaining the same convergence rate that is solely controlled by the initial SSE value. We illustrate our findings with a simulation study for spherical Gaussian mixtures and a real-world image segmentation dataset.

This study presents a theoretical analysis of partitional clustering on networks, analyzing both hard and soft assignment schemes with different objective functions. Cluster centers are not restricted to vertices but can also be located along the edges. We examine four key models: P-Median (PMP) and Sum of Squares Clustering (SSC) under hard assignment, and Probabilistic Distance Clustering (PDC) and Fuzzy C-Means (FCM) under soft assignment. Through mathematical analysis, we uncover structural properties that differentiate these models, such as the significance of assignment bottleneck points and the role of vertex-restricted solutions in determining optimal cluster centers. Our findings reveal that, while SSC and FCM can yield optimal centers along edges, PMP and PDC inherently favor vertex placement, leading to insights into clustering behavior on networks. These insights offer new directions for designing efficient algorithms and have implications ranging from facility location and network design to clustering on the embedding graphs that power similarity search in modern retrieval systems.

Search Trajectory Networks (STNs) are a graph-based tool for visualizing and characterizing the behavior of optimization algorithms. STNs' reliance on discretization of the search space has largely confined them to low-dimensional or combinatorial settings. We introduce a methodology for constructing STNs in semantic spaces, defined as the space of a model's predictions on a fixed sample set. Our approach discretizes semantic vectors and aggregates them into network nodes via agglomerative clustering with complete linkage under a normalized Hamming distance. Since any predictor can be summarized by its semantic vector, this method enables comparison of learning dynamics across otherwise incomparable algorithm families. We apply semantic space STNs to classification and regression tasks solved using different machine learning algorithms, recovering known qualitative differences between them. Additionally, we use semantic space STNs to study neural network generalization by contrasting standard training with the label randomization regime of Zhang et al. (2017). The resulting STNs exhibit consistent structural differences, training on real labels produces denser, more efficient and more centralized graphs than training on shuffled labels. Together, our results show that semantic space STNs capture functional training dynamics arising from the interaction between learning algorithms and data, providing a tool for analyzing and comparing learning dynamics across machine learning models and training regimes.

In the Big Data era, the scalability of clustering algorithms constitutes a key challenge. Traditional density-based methods (e.g., DBSCAN) offer robustness to noise and the ability to detect non-linear clusters, yet their quadratic time complexity $O(N^2)$ drastically limits their applicability. Conversely, partitional algorithms (e.g., K-Means), with their linear complexity $O(N)$, impose sphericity on the resulting groups and fail in the presence of outliers. This paper presents K-SCAN -- a novel hybrid algorithm that optimizes this trade-off. The method integrates preliminary vector quantization (stochastic Mini-Batch K-Means) to extract a reduced set of weighted micro-clusters, followed by a subsequent density-based structural analysis. Empirical evaluation on datasets of up to $10^6$ samples confirms the linear computational complexity of the proposed solution. K-SCAN achieves more than a 3-fold speed-up over the hierarchical BIRCH algorithm, avoiding the costly management of tree-based structures. The method precisely identifies non-linear manifolds while maintaining structural stability (Adjusted Rand Index > 0.99), even with noise levels reaching 55% of the data volume. The main limitation of the proposed algorithm, which could not be fully eliminated in the present study, remains its susceptibility to over-smoothing and its difficulty in separating clusters with highly heterogeneous local density. In complex visual spaces, this can lead to the loss of the finest topological details.

In this work, we propose K-SurvMeans, a novel extension of K-Means for clustering survival data. The method explicitly uses the survival outcome in the clustering process to optimize cluster centers, thereby maximizing pairwise survival differences between clusters. The objective function encourages the clusters to be well-separated from the survival perspective. Since the resulting optimization problem is non-differentiable, we employ the Particle Swarm algorithm for the Optimization process. To further improve flexibility and mitigate the curse of dimensionality, we extend the framework to operate in a learned low-dimensional latent space obtained via a dimensionality reduction. This allows the method to capture better-separated clusters and enhance optimization efficiency by reducing the search space. Experiments on multiple publicly available benchmark survival datasets demonstrate that K-SurvMeans consistently yields clusters with improved separation in survival distributions compared to existing deep learning-based survival clustering methods.

Many existing clustering methods are designed based on a set-oriented definition---a cluster is a set of similar points---relying a point-to-point similarity function to find similar points. This works well for compact clusters, but clustering performance can deteriorate badly when cluster shapes are irregular, and densities or sizes vary between clusters. Recent `Cluster-as-Distribution' (CaD) clustering has been shown to discover these generic types of clusters in practice by treating each cluster as a set of independent and identically distributed points generated from some unknown distribution via a greedy search, achieving a clustering objective equivalent to that of Spectral Clustering, but with better clustering outcomes without eigen-decomposition. However, a theoretical analysis of this phenomenon is still lacking. Our analyses are from two angles. First, we analyze the approximation error between the true and empirical distribution embeddings. Second, we show that the greedy search employed to achieve the CaD clustering objective can be mapped to a partition matroid---yielding greedy optimality. These yield a near-optimality guarantee for the CaD clustering objective, with regret controlled by the approximation error. This is the first analysis that explains why CaD clustering via greedy search can discover clusters of arbitrary shapes, densities and sizes (where all set-oriented clustering methods have failed to discover) when the estimated cluster embeddings faithfully approximate the underlying cluster distributions.

Machine unlearning, which aims to remove the influence of specific training data from a trained model, is a key requirement for privacy, accountability, and adaptive deployment. We argue that many unlearning methods are vulnerable to a simple clustering attack, which can recover class structure in an unsupervised manner, limiting their suitability for continual deployment where removal requests must be handled reliably on demand. To address this, we propose DECAF (DE-Clustering for Adaptive Forgetting), a post-hoc method that operates only on the forget set and is designed to break the cluster. DECAF combines input noise, confidence suppression, and entropy-based output diversification to disrupt the residual feature-space structure associated with forgotten data. On CIFAR-10 with ResNet-18, DECAF attains 0.10% forget-class accuracy, 79.4% retain accuracy, and an AUS of 0.88, surpassing all other baselines. In cluster-based analysis, it attains performance comparable to that of unlearning methods that use the full training set, while being significantly more efficient. Code: https://github.com/ale256/representation_unlearning.

Scalar metrics are often used to evaluate clusterings against known classes, but they can obscure a fundamental trade-off: clusterings should be informative about class labels while avoiding unnecessary fragmentation. Here we describe normalized scores of cluster homogeneity and parsimony that quantify this trade-off. These scores build on the information bottleneck principle, modified to not reward lossy compression. We show by example and mathematical proof that our definitions of these scores have the intuitive property of varying monotonically under cluster refinement in contrast to related proposals. Extending the information-theoretic framework beyond Shannon entropies, we furthermore derive set-matching and pair-based counterparts of the homogeneity and parsimony scores. These unify commonly used evaluation criteria and show that, in the pair-based setting, the homogeneity-parsimony trade-off recovers the receiver operating characteristic of binary classifiers. We demonstrate the framework's utility for feature selection and algorithm comparison, illustrating how considering scores jointly can clarify clustering operating points and identify Pareto-optimal solutions.

Scaling LLM-based applications to millions of users is bottlenecked by the inference cost and latency of modern foundation models. A natural fix is to cluster the inputs and call the LLM only on cluster representatives, letting other members inherit the output -- but this is only safe if each member is measurably close to its representative. Existing clustering methods do not offer such per-sample quality control at scale: none jointly guarantee a minimal within-cluster similarity, exact matching of categorical attributes, and scalability to tens of millions of samples. We propose a two-stage algorithm that generates initial clusters with Mini-batch K-Means, then greedily selects representatives within each initial cluster -- a step equivalent to the Johnson-Chvatal heuristic for Set Cover over alpha-balls in embedding space. The algorithm enforces the similarity and attribute guardrails exactly by construction, and runs in $O(nd + n^2 d/K)$ time and $O(nd + n^2/K^2)$ memory for $n$ samples, feature dimension $d$, and $K$ initial clusters -- linear in $n$ when $K$ grows proportionally with $n$. We provide benchmarks against common clustering methods on internal and public datasets: our method not only delivers per-sample guardrails but also runs 10-1000x faster and scales to data sizes where most standard methods become intractable. Deployed on 38 million customers for a persona-based recommender, the clustering method cut downstream cost and latency by 50-fold while preserving personalization and unblocked the production launch.

In this paper, we present SCPP (Soft Clustering Python Package), an open-source Python framework for soft clustering. SCPP establishes a canonical, scikit-learn-compatible estimator interface that standardizes model training, prediction, membership representation, evaluation, and benchmarking across heterogeneous soft clustering methods, including fuzzy, probabilistic, graph-based, matrix factorization, and deep learning methods. The framework currently integrates 40 representative algorithms together with a comprehensive benchmarking comprising datasets, clustering quality metrics, and standardized runtime, memory, and scalability evaluation. SCPP further provides extensive documentation, practical examples, automated testing, and seamless integration with the scientific Python ecosystem, enabling reproducible experimentation and straightforward extension with new algorithms. The source code is publicly available at https://github.com/soft-clustering/soft-clustering.

Fair clustering aims to make cluster assignments independent of sensitive attributes, but this goal becomes challenging when multiple sensitive attributes jointly define many subgroups. In such settings, directly extending existing fair clustering algorithms is computationally expensive or numerically unstable, especially when the number of subgroups grows exponentially and some subgroups contain only a few instances. To address these challenges, we define a subgroup-fairness gap for clustering and derive a covariance-based surrogate that exactly matches this gap. We then introduce a continuous relaxation of the surrogate, enabling efficient gradient-based optimization and yielding our proposed algorithm, COVA-FC. We also show that subgroup fairness alone does not imply marginal fairness, and extend our framework to capture a subgroup-marginal-fairness gap. Experiments on benchmark datasets show that COVA-FC achieves competitive cost-fairness trade-offs and improves computational efficiency over existing baselines in both subgroup and higher-order marginal settings.

Medical image segmentation models require both high accuracy and lightweight design to accommodate real-world medical applications. The deployment of these models on resource-limited medical platforms remains a significant challenge due to their high computational and parameter requirements. Existing pruning methods for model compression mostly overlook the intrinsic connections and similarity between the internal structures of complex deep neural networks. As a result, compressed models may not effectively retain the basic features of the pretrained network. To solve this problem, we propose a hierarchical clustering compression method for medical image segmentation models (MIS-HCC). This approach employs hierarchical clustering to partition channels and fuse their parameters efficiently. Specifically, it leverages the Wasserstein distance to represent similarity of channels within layers of pre-trained network, forming a similarity matrix that guides the clustering process. Channels within each cluster are then fused to produce a compressed network. Experimental results on three medical image datasets application demonstrate that MIS-HCC outperforms the state-of-the-art methods in both accuracy and compression efficiency, offering an effective solution for deploying medical image segmentation models on resource-limited medical platforms.

In many applications of matching, the point clouds to be matched are not merely unstructured sets of points but rather samples from distributions with an intrinsic cluster structure. In such cases, as individual points are often interchangeable within a coherent region, finding a robust region-to-region alignment is more desirable than establishing a precise point-to-point correspondence. To this end, we propose a novel approach for cluster-aware matching based on Laplacian Optimal Transport (LapOT). The key idea is to regularize the optimal transport problem with quadratic Laplacian terms constructed from similarity graphs of the point clouds, which encourages the optimal coupling to respect the cluster structure of both point sets. We also introduce Refined Simultaneous Clustering (RSC), a method that leverages the cluster-aware coupling obtained from LapOT to produce consistent partitions across the point sets, which can overcome the limitations of independent clustering and yield more stable and interpretable results. We demonstrate the effectiveness of our approach through theoretical analysis and empirical experiments, showing that LapOT indeed produces cluster-aware matching that leads to more consistent and meaningful alignments between point clouds.

Big data clustering remains challenging: the Minimum Sum-of-Squares Clustering (MSSC) problem underlying K-means is NP-hard, and existing methods either reach poor local minima or require prohibitive metaheuristic hybrids. We target arbitrarily tall data: a fixed feature space may contain arbitrarily many, possibly infinitely many, observations, while the algorithm accesses only finite random samples. We propose Big-means++, an algorithm achieving scalability and global-search quality by curating inputs to MSSC optimization on big data. It orchestrates local K-means refinements into a data-native global search for big data clustering. Rather than optimizing the full-data MSSC objective, Big-means++ traverses sample-induced surrogate landscapes. Each sample defines a distinct empirical MSSC approximation with a perturbed local-optimum structure, turning sample-to-sample variation into a global-search mechanism. Unlike Big-means, a flowing-incumbent strategy propagates centroid state across empirical landscapes through K-means refinements on fresh samples without rollback to a best-so-far solution. This increases mobility and favors stable, high-quality configurations across approximations of the full-data structure. A new shaking mechanism varies sample size geometrically, broadening the surrogate landscapes explored across resolution scales, accounting for cluster imbalance, and improving solution quality. A competitive multi-agent system asynchronously explores independent sampled landscapes, transforming diverse stochastic trajectories into collective search intelligence. Automatic convergence detection stops each agent after attaining a high-quality solution but before further search risks degrading it, while providing a universal speed-quality control. Experiments on 22 datasets against 11 competing algorithms demonstrate the effectiveness, efficiency, and robustness of Big-means++.

Face recognition models represent each face as an embedding vector on the unit hypersphere by clustering embeddings of the same identity while pushing different identities apart through angular-margin losses. Because these losses act only on training identities, non-member identities may form clusters with different geometric properties. In this paper, we quantify the magnitude of this difference and what training-time factors control it. We compute four statistics based on cluster geometry across 180 face recognition models in a factorial design over IResNet backbone size, loss head, training duration, and the number of training identities, and evaluate each configuration on nine benchmarks. Our results indicate that the number of training identities has the largest effect on member/non-member separability, while backbone and loss head contribute far less, and that, on a same-domain held-out reference, the geometric membership signal decreases monotonically as more identities are added to training. We provide an analysis of cross-domain (pose, age, quality, ethnicity) non-member benchmarks and report that these inflate the apparent membership signal. Finally, we fuse all four statistics with a learned classifier to reveal additional membership information beyond the best individual statistic.

Counterfactual explanations provide local, interpretable insight by identifying changes to an input that would alter its assigned outcome. Although well established in supervised learning, their extension to clustering is less direct, since cluster assignments are unlabeled and governed by the geometry of the partition. This paper introduces VoICE, a Voronoi-Induced Counterfactual Explainability framework for feature-weighted $k$-means clustering. Rather than treating cluster change as a crossing of a single pairwise centroid boundary, VoICE formulates counterfactual generation as projection onto the full weighted Voronoi region of a target cluster, incorporating feature weights directly into both the clustering geometry and the counterfactual objective to yield least-cost and parsimonious explanations under actionability constraints. Target regions are further intersected with data-derived bounds and homothetically contracted towards their centroids, limiting extrapolation and boundary sensitivity. VoICE consistently produces valid target-cluster membership, across several benchmark datasets, where the leading pairwise baseline does not.

Centroid neural network (CentNN) is an unsupervised competitive learning algorithm in which centroid splitting is triggered only after strict local stabilization, often leading to prolonged low-movement training phases before model expansion. This report proposes FastCentNN, an accelerated variant that addresses this inefficiency by introducing an early splitting strategy based on the total centroid movement per epoch, which serves as a training entropy proxy. As a result, FastCentNN reduces unnecessary reassignment epochs while preserving the original winner-loser learning dynamics. FastCentNN supports both absolute and stage-relative movement thresholds, allowing the splitting criterion to remain either fixed or adaptive throughout training. Experiments on some benchmark datasets show that FastCentNN consistently achieves clustering quality comparable to CentNN while reducing runtime by up to 16% on synthetic 2D datasets and about 5% on high-dimensional datasets. FastCentNN therefore provides a practical and efficient drop-in replacement for CentNN, retaining its online adaptive learning behavior while offering a simple and interpretable speed-stability trade-off through configurable splitting thresholds.

During wind farm operation, Supervisory Control and Data Acquisition (SCADA) systems record numerous anomalies, transients, and specific operational modes, leading to large datasets. However, for a wide range of applications, only measurements corresponding to normal operation are required and, therefore, the SCADA data must be filtered. For this purpose, several methods have been proposed to automate and replace manual filtering conducted by experts via visual inspection of the data. In this paper, we compare the filtering accuracy of multiple clustering algorithms against manual filtering, introducing evaluation metrics that are suitable for unlabeled data and robust across potential applications. Based on the results, we provide recommendations for generalizing model calibration to different datasets and discuss potential use cases for each model. The models are applied to the SCADA data of three turbines of an existing offshore wind farm, using 10-minute statistics across multiple data channels. In addition to the anomalies and operational modes typically recorded, the dataset presents a large number of non-evident outliers due to several field tests. Overall, the results highlight the importance of extending the analysis beyond the power curve, both in feature selection and in the design of evaluation metrics. In most cases, cluster-based methods are able to detect both evident and subtle outliers, achieving higher accuracy than manual filtering. However, the accuracy and the amount of data retained vary considerably depending on the model, and expert involvement remains necessary, though to a reduced extent compared to manual filtering.

Traffic forecasting is highly challenging due to complex and nonlinear spatial and temporal dependencies. Self-attention mechanisms have been widely adopted to model dynamic and long-range dependencies, achieving state-of-the-art performance, but suffer from limited scalability due to quadratic computational and memory complexity. To address this, we propose an Efficient Multi-Attention Graph Network (EMAGN) that linearises the spatial attention mechanism itself, inspired by the theory of fast high-dimensional Gaussian filtering. Two learned clustering matrices C_k and C_v adaptively group key and value vectors into M super-clusters, reducing complexity from O(N^2 d) to O(NMd) without sacrificing the flexibility of attention for dynamic dependency modelling. Experimental results on PEMS-BAY and METR-LA show that EMAGN achieves accuracy within 2.7-3.2% MAE of full-attention GMAN while reducing training time by 32%, inference time by 38%, and GPU memory by 58%. Critically, at K=16 attention heads, full-attention GMAN runs out of memory on a standard 11 GB GPU entirely while EMAGN continues to operate, demonstrating a categorical expansion of feasible model configurations. EMAGN also surpasses Linformer and Performer in both accuracy and efficiency within the same backbone, owing to its traffic-network-aware adaptive clustering.

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.

Aligning robot policies with human preferences is essential for deployment to diverse end users. In per-user alignment approach, preference feedback is often sparse, so learning becomes unstable and vulnerable to human preference noise, and a growing number of individualized policies makes validation difficult before deployment. A single shared policy approach to user alignment avoids this cost but fails to capture heterogeneous preferences and often neglects minority preferences. To address these challenges, we introduce Preference-based REward Clustering (PREC), a novel framework that learns a compact set of policies from binary preference labels provided by diverse users. From a dataset of user trajectories and their preference labels, PREC first sets the labels aside and aggregates trajectories across users to learn a population-level shared trajectory encoder, alleviating limited per-user coverage and avoiding label noise during representation learning. Using this representation, PREC jointly assigns users to preference-coherent clusters and learns a representative reward model per cluster using preference labels, from which a policy is optimized for each cluster. Clustering similar users compensates for the limited number of labels available from each user and mitigates the effect of label noise. At the same time, maintaining a manageable number of reward models reduces the validation burden at deployment. Experiments across diverse simulated locomotion environments show that PREC groups users who label different trajectory subsets into preference-coherent clusters more accurately than baseline methods. Under sparse and noisy feedback, policies trained with PREC improve all three social welfare metrics over an existing single shared-policy user-alignment approach and even outperform per-user alignment approaches.

Pseudo-labeling based on Optimal Transport (OT) has become an effective mechanism for enhancing short text clustering. Existing OT methods are short in modeling semantic consistencies between samples, which may assign different pseudo-labels to semantically similar samples. These erroneous pseudo-labels can cause the model to produce inferior clusters. This paper proposes a novel short text clustering framework, which remedies the neglect of semantic consistency in existing OT methods, generating reliable pseudo-labels to facilitate clustering. Specifically, the proposed approach first designs an instance-level attention mechanism to capture semantic relationships between samples, which are then integrated into the OT formulation to endow the transport process with neighborhood semantic awareness. By solving the proposed OT formulation, reliable pseudo-labels are obtained that simultaneously account for sample-to-sample semantic consistency and sample-to-cluster global structure information. These pseudo-labels are then used as supervisory signals to guide the model to achieve accurate clustering. Extensive experiments demonstrate that the proposed approach outperforms state-of-the-art methods. The code is available at: \href{https://github.com/YZH0905/CAOT-STC}{https://github.com/YZH0905/CAOT-STC}.

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.

The k-means++ algorithm is commonly restarted multiple times to avoid poor local optima, yet the number of restarts is almost always chosen arbitrarily and applied uniformly regardless of data set difficulty. This undermines any comparison relying on such a choice and wastes computation on easy data sets while potentially under-serving hard ones. We introduce GTRC, a restart criterion combining a Good-Turing estimate, a proven unconditional bound, and a confidence-based bound on the probability that a further restart would improve on the current result, stopping once this probability falls below a user-specified tolerance $\varepsilon$. Across 36 data sets, GTRC reached clustering quality competitive with well-chosen fixed restart counts, while the number of restarts used varied considerably and appropriately with data set difficulty, governed by an interpretable, data-dependent signal rather than a fixed rule. GTRC offers a principled and reportable alternative to fixing the number of $k$-means++ restarts in advance. Software:https://github.com/RCdeAmorim/Good-Turing-Restart-Criterion.

Recent algorithmic advances have made directed acyclic graph (DAG) structure learning scalable for causal discovery. Yet, the currently available techniques assume a completely homogeneous population, precluding their application to clustered data where cluster-specific variations (e.g., patient-specific effects) are common. We address this issue by introducing a new approach that estimates a global structure while accounting for local cluster-level effects. The key idea is to extend the fixed- and random-effects framework of classical mixed models to the structure learning setting. Towards this end, we present a differentiable graph coupling mechanism that guarantees the union of the fixed- and random-effects graphs remains acyclic. Computationally, we provide a provably convergent first-order method and leverage efficient batched updates across clusters. Statistically, we establish identifiability of the model and show that our approach recovers the true structure asymptotically. In experiments on real and synthetic data, our proposal detects dependencies missed by alternative estimators, underscoring its value for structure learning in clustered settings.

Intent detection is a critical task that bridges human intents and system actions in human-machine interaction systems. However, there still exist challenges for detecting out-of-scope (OOS) intents. (i) The traditional methods view the OOS intent detection as a multi-class classification, then the detection accuracy decreases as the class number of the known intents increases; (ii) LLM-embedding methods require large parameters, that makes them difficult to train and practically deploy. Thus, this work proposes a multi-cluster boundary learning method to detect OOS intents via MiniLM embedding (i.e., all-MiniLM-L6-v2) in an one-class classification workflow. The method learns the boundaries of multi-cluster embeddings generated by MiniLM from the training utterances, and then rejects the out-of-domain utterances as OOS intents. Experiments are conducted on public CLINC150, StackOverflow and Banking77 datasets. The results show that the method achieves the state-of-the-art OOS intent detection performance compared the other baselines. Ablation studies are also conducted and the results show that the used MiniLM can better adapt to the workflow and utterance embedding requirements. The code is available at supplementary materials.

A variety of self-supervised image clustering approaches are invented in the past years. However, all dominant approaches are exploitative: The direction of parameter updates is determined by known states (observed input samples and existing parameters). We propose an explorative self-supervised learning framework that steps out of this zone. We define a surprise score that measures how unlikely the model's output representation is, assuming that all pixels are i.i.d. random noise. Maximizing the surprise score forces the deep learning model to reject the random noise null hypothesis, or equivalently, to discover non-randomness from data. Also, we propose a fundamental assumption: a surprise score cannot, in general, be fully optimized by exploitative optimization approaches. Thus, we propose the converge-to-surprise scheme to optimize a model: an evolution-strategy (ES) outer loop, which maximizes the surprise score using the mutation-selection mechanism, paired with a periodic gradient-descent inner loop, which uses the surprising clusters already discovered by ES as surrogate targets. On simple image benchmarks, our framework trained from scratch achieves new state-of-the-art results in non-parametric self-supervised image clustering --- the strictest deep-clustering setting, where the number of classes is unknown during training.