Attribute-missing graph clustering has emerged as a significant unsupervised task, where only attribute vectors of partial nodes are available and the graph structure is intact. The related models generally follow the two-step paradigm of imputation and refinement. However, most imputation approaches fail to capture class-relevant semantic information, leading to sub-optimal imputation for clustering. Moreover, existing refinement strategies optimize the learned embedding through graph reconstruction, while neglecting the fact that some attributes are uncorrelated with the graph. To remedy the problems, we establish the Clustering-oriented Generative Imputation with reliable Refinement (CGIR) model. Concretely, the subcluster distributions are estimated to reveal the class-specific characteristics precisely, and constrain the sampling space of the generative adversarial module, such that the imputation nodes are impelled to align with the correct clusters. Afterwards, multiple subclusters are merged to guide the proposed edge attention network, which identifies the edge-wise attributes for each class, so as to avoid the redundant attributes in graph reconstruction from disturbing the refinement of overall embedding. To sum up, CGIR splits attribute-missing graph clustering into the search and mergence of subclusters, which guides to implement node imputation and refinement within a unified framework. Extensive experiments prove the advantages of CGIR over state-of-the-art competitors.

Bayesian clustering accounts for uncertainty but is computationally demanding at scale. Furthermore, real-world datasets often contain missing values, and simple imputation ignores the associated uncertainty, resulting in suboptimal results. We present Cluster-PFN, a Transformer-based model that extends Prior-Data Fitted Networks (PFNs) to unsupervised Bayesian clustering. Trained entirely on synthetic datasets generated from a finite Gaussian Mixture Model (GMM) prior, Cluster-PFN learns to estimate the posterior distribution over both the number of clusters and the cluster assignments. Our method estimates the number of clusters more accurately than handcrafted model selection procedures such as AIC, BIC and Variational Inference (VI), and achieves clustering quality competitive with VI while being orders of magnitude faster. Cluster-PFN can be trained on complex priors that include missing data, outperforming imputation-based baselines on real-world genomic datasets, at high missingness. These results show that the Cluster-PFN can provide scalable and flexible Bayesian clustering.

Understanding causal heterogeneity is essential for scientific discovery in domains such as biology and medicine. However, existing methods lack causal awareness, with insufficient modeling of heterogeneity, confounding, and observational constraints, leading to poor interpretability and difficulty distinguishing true causal heterogeneity from spurious associations. We propose an unsupervised framework, HCL (Interpretable Causal Mechanism-Aware Clustering with Adaptive Heterogeneous Causal Structure Learning), that jointly infers latent clusters and their associated causal structures from mixed-type observational data without requiring temporal ordering, environment labels, interventions or other prior knowledge. HCL relaxes the homogeneity and sufficiency assumptions by introducing an equivalent representation that encodes both structural heterogeneity and confounding. It further develops a bi-directional iterative strategy to alternately refine causal clustering and structure learning, along with a self-supervised regularization that balance cross-cluster universality and specificity. Together, these components enable convergence toward interpretable, heterogeneous causal patterns. Theoretically, we show identifiability of heterogeneous causal structures under mild conditions. Empirically, HCL achieves superior performance in both clustering and structure learning tasks, and recovers biologically meaningful mechanisms in real-world single-cell perturbation data, demonstrating its utility for discovering interpretable, mechanism-level causal heterogeneity.

Medical images are inherently high-resolution and contain locally varying structures crucial for diagnosis. Efficient compression must preserve diagnostic fidelity while minimizing redundancy. Low-rank matrix approximation (LoRMA) techniques have shown strong potential for image compression by capturing global correlations; however, they often fail to adapt to local structural variations across regions of interest. To address this, we introduce an adaptive LoRMA, which partitions a medical image into overlapping patches, groups structurally similar patches into clusters using k-means, and performs SVD within each cluster. We derive the overall compression factor accounting for patch overlap and analyze how patch size influences compression efficiency and computational cost. While applicable to any data with high local variation, we focus on medical imaging due to its pronounced local variability. We evaluate and compare our adaptive LoRMA against global SVD across four imaging modalities: MRI, ultrasound, CT scan, and chest X-ray. Results demonstrate that adaptive LoRMA effectively preserves structural integrity, edge details, and diagnostic relevance, measured by PSNR, SSIM, MSE, IoU, and EPI. Adaptive LoRMA minimizes block artifacts and residual errors, particularly in pathological regions, consistently outperforming global SVD in PSNR, SSIM, IoU, EPI, and achieving lower MSE. It prioritizes clinically salient regions while allowing aggressive compression in non-critical regions, optimizing storage efficiency. Although adaptive LoRMA requires higher processing time, its diagnostic fidelity justifies the overhead for high-compression applications.

We study the problem of constructing coresets for $(k, z)$-clustering when the input dataset is corrupted by stochastic noise drawn from a known distribution. In this setting, evaluating the quality of a coreset is inherently challenging, as the true underlying dataset is unobserved. To address this, we investigate coreset construction using surrogate error metrics that are tractable and provably related to the true clustering cost. We analyze a traditional metric from prior work and introduce a new error metric that more closely aligns with the true cost. Although our metric is defined independently of the noise distribution, it enables approximation guarantees that scale with the noise level. We design a coreset construction algorithm based on this metric and show that, under mild assumptions on the data and noise, enforcing an $\varepsilon$-bound under our metric yields smaller coresets and tighter guarantees on the true clustering cost than those obtained via classical metrics. In particular, we prove that the coreset size can improve by a factor of up to $\mathrm{poly}(k)$, where $n$ is the dataset size. Experiments on real-world datasets support our theoretical findings and demonstrate the practical advantages of our approach.

Traditional clustering algorithms often struggle with high-dimensional and non-uniformly distributed data, where low-density boundary samples are easily disturbed by neighboring clusters, leading to unstable and distorted clustering results. To address this issue, we propose a Group-driven Clustering via Gravitational Attraction and Optimization (GCAO) algorithm. GCAO introduces a group-level optimization mechanism that aggregates low-density boundary points into collaboratively moving groups, replacing the traditional point-based contraction process. By combining local density estimation with neighborhood topology, GCAO constructs effective gravitational interactions between groups and their surroundings, enhancing boundary clarity and structural consistency. Using groups as basic motion units, a gravitational contraction strategy ensures globally stable and directionally consistent convergence. Experiments on multiple high-dimensional datasets demonstrate that GCAO outperforms 11 representative clustering methods, achieving average improvements of 37.13%, 52.08%, 44.98%, and 38.81% in NMI, ARI, Homogeneity, and ACC, respectively, while maintaining competitive efficiency and scalability. These results highlight GCAO's superiority in preserving cluster integrity, enhancing boundary separability, and ensuring robust performance on complex data distributions.

Cross-linguistically, native words and loanwords follow different phonological rules. In English, for example, words of Germanic and Latinate origin exhibit different stress patterns, and a certain syntactic structure, double-object datives, is predominantly associated with Germanic verbs rather than Latinate verbs. As a cognitive model, however, such etymology-based generalizations face challenges in terms of learnability, since the historical origins of words are presumably inaccessible information for general language learners. In this study, we present computational evidence indicating that the Germanic-Latinate distinction in the English lexicon is learnable from the phonotactic information of individual words. Specifically, we performed an unsupervised clustering on corpus-extracted words, and the resulting word clusters largely aligned with the etymological distinction. The model-discovered clusters also recovered various linguistic generalizations documented in the previous literature regarding the corresponding etymological classes. Moreover, our findings also uncovered previously unrecognized features of the quasi-etymological clusters.

We study unsupervised clustering of documents at both the category and template levels using frozen multimodal encoders and classical clustering algorithms. We systematize a model-agnostic pipeline that (i) projects heterogeneous last-layer states from text-layout-vision encoders into token-type-aware document vectors and (ii) performs clustering with centroid- or density-based methods, including an HDBSCAN + $k$-NN assignment to eliminate unlabeled points. We evaluate eight encoders (text-only, layout-aware, vision-only, and vision-language) with $k$-Means, DBSCAN, HDBSCAN + $k$-NN, and BIRCH on five corpora spanning clean synthetic invoices, their heavily degraded print-and-scan counterparts, scanned receipts, and real identity and certificate documents. The study reveals modality-specific failure modes and a robustness-accuracy trade-off, with vision features nearly solving template discovery on clean pages while text dominates under covariate shift, and fused encoders offering the best balance. We detail a reproducible, oracle-free tuning protocol and the curated evaluation settings to guide future work on unsupervised document organization.

Federated clustering (FC) aims to discover global cluster structures across decentralized clients without sharing raw data, making privacy preservation a fundamental requirement. There are two critical challenges: (1) privacy leakage during collaboration, and (2) robustness degradation due to aggregation of proxy information from non-independent and identically distributed (Non-IID) local data, leading to inaccurate or inconsistent global clustering. Existing solutions typically rely on model-specific local proxies, which are sensitive to data heterogeneity and inherit inductive biases from their centralized counterparts, thus limiting robustness and generality. We propose Omni Federated Clustering (OmniFC), a unified and model-agnostic framework. Leveraging Lagrange coded computing, our method enables clients to share only encoded data, allowing exact reconstruction of the global distance matrix--a fundamental representation of sample relationships--without leaking private information, even under client collusion. This construction is naturally resilient to Non-IID data distributions. This approach decouples FC from model-specific proxies, providing a unified extension mechanism applicable to diverse centralized clustering methods. Theoretical analysis confirms both reconstruction fidelity and privacy guarantees, while comprehensive experiments demonstrate OmniFC's superior robustness, effectiveness, and generality across various benchmarks compared to state-of-the-art methods. Code will be released.

Fair graph clustering seeks partitions that respect network structure while maintaining proportional representation across sensitive groups, with applications spanning community detection, team formation, resource allocation, and social network analysis. Many existing approaches enforce rigid constraints or rely on multi-stage pipelines (e.g., spectral embedding followed by $k$-means), limiting trade-off control, interpretability, and scalability. We introduce \emph{DFNMF}, an end-to-end deep nonnegative tri-factorization tailored to graphs that directly optimizes cluster assignments with a soft statistical-parity regularizer. A single parameter $λ$ tunes the fairness--utility balance, while nonnegativity yields parts-based factors and transparent soft memberships. The optimization uses sparse-friendly alternating updates and scales near-linearly with the number of edges. Across synthetic and real networks, DFNMF achieves substantially higher group balance at comparable modularity, often dominating state-of-the-art baselines on the Pareto front. The code is available at https://github.com/SiamakGhodsi/DFNMF.git.