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.
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:2603.03188v3 Announce Type: replace-cross Abstract: Density-based clustering is a well-established framework that defines clusters through topological or geometric features of the data-generati...
arXiv:2609.26748v1 Announce Type: cross Abstract: Clustering is an unsupervised learning technique that partitions unlabeled data into groups. Most existing methods require user-specified parameters,...
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:2609.36762v1 Announce Type: new Abstract: Federated clustering methods that do not require the global number of clusters $K$ still assume that each client knows its local number $K_g$. This ass...
arXiv:2610.09153v1 Announce Type: cross Abstract: Contemporary data in many scientific domains, such as images, media streams, biomedical omics, are naturally modeled as probability distributions in...
The paper introduces T-ARC, a clustering algorithm that integrates topological information into the K‑means objective by coupling a data‑fidelity term with a graph‑cut penalty. The latent graph is modeled as a random realization from a Stochastic Block Model, whose parameter is optimized via Distributionally Robust Optimization, using a persistence‑based similarity matrix derived from zero‑dimensional persistent homology. Experiments on synthetic non‑convex data and Fashion‑MNIST subsets demonstrate that T‑ARC recovers latent topological structures and outperforms K‑means on curved and interleaved clusters while remaining competitive and more stable on real data.
arXiv:2609. 30477v1 Announce Type: cross Abstract: Exact Euclidean \(K\)-means partitions \(n\) observations into \(K\) unlabelled clusters, but the unrestricted search is generally exponential.
arXiv:2411. 01576v3 Announce Type: replace Abstract: The explainable clustering problem was first posed by Moshkovitz et al.