arXiv:2607. 24237v1 Announce Type: new Abstract: 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.
arXiv:2608. 14215v1 Announce Type: new Abstract: Constrained optimization extends classical optimization by integrating side information, making it widely applicable across scientific and engineering domains.
arXiv:2607. 24537v1 Announce Type: new Abstract: In the Big Data era, the scalability of clustering algorithms constitutes a key challenge.
arXiv:2606. 18833v1 Announce Type: new Abstract: This paper introduces a semi-supervised clustering framework grounded in the statistical duality between grouping principles and anomaly detection.
arXiv:2608. 06990v1 Announce Type: cross Abstract: Clustering is a fundamental data mining technique for pattern recognition through unsupervised learning.
arXiv:2411. 01576v3 Announce Type: replace Abstract: The explainable clustering problem was first posed by Moshkovitz et al.
arXiv:2608. 19067v1 Announce Type: cross Abstract: The empirical success of diffusion models in generative modelling has motivated theoretical work, including quantitative error bounds and qualitative analyses that characterise the different phases of denoising.
arXiv:2512. 16558v3 Announce Type: replace Abstract: Clustering is a cornerstone of modern data analysis.
arXiv:2607. 04949v1 Announce Type: new Abstract: We study the problem of k-means clustering on large datasets.
arXiv:2607. 01945v1 Announce Type: cross Abstract: The classical $k$-means clustering cannot be directly used to incomplete data, and existing $k$-means-based clustering for missing data primarily focus on improving the practical accuracy of clustering, whereas most of them lack theoretical guarantees in the asymptotic sense.
The paper introduces the Universal Clustering Problem (UCP), a framework that captures the optimisation core common to many clustering methods by maximizing a polynomial‑time computable partition utility over a finite metric space. It proves UCP is NP‑hard through reductions from graph colouring and exact cover by 3‑sets, showing that popular algorithms such as k‑means, GMMs, DBSCAN, spectral clustering, and affinity propagation inherit this intractability. The authors argue that this unified hardness explains typical failure modes—like local optima and greedy merge traps—and suggest moving toward stability‑aware objectives and interaction‑driven formulations with explicit guarantees.
arXiv:2505. 04346v2 Announce Type: replace Abstract: Clustering aims at partitioning data points into groups of similar objects without knowing about the class labels.