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.
By Angshul Majumdar
The paper formalizes a geometric tradeoff between ambient separation and sampling gaps to determine when distinct manifold components can be reliably separated in clustering. It introduces a threshold phenomenon for mutual‑k‑nearest‑neighbor graphs, defining an uncertainty zone where the number of clusters cannot be identified. The authors propose Manifold‑Based Clustering (MBC), which outputs a bracket interval quantifying this uncertainty rather than forcing a single cluster count.
By Savik Kinger, Luciano Dyballa, Steven W. Zucker
arXiv:2606. 05230v1 Announce Type: cross Abstract: Selecting a clustering algorithm and its hyperparameters without labels is a common difficulty in engineering machine learning pipelines that work with unsupervised analysis of sensor, image, or process data.
By Mahdi Shamsi, Soosan Beheshti
arXiv:2502. 08397v3 Announce Type: replace-cross Abstract: Clustering is a fundamental technique in data analysis and machine learning, used to group similar data points together.
By Anna Livia Croella, Veronica Piccialli, Antonio M. Sudoso
arXiv:2607. 04949v1 Announce Type: new Abstract: We study the problem of k-means clustering on large datasets.
By Cristian Boldrin, Fabio Vandin
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.
By Nassir Mohammad