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Affinity Graph Connectivity in Convex Clustering
Sam Rosen, J · 2026-05-26 · via cs.LG updates on arXiv.org

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Abstract:We generalize finite-sample bounds for convex clustering to the setting where affinity weights appearing in the objective correspond to a general connected graph. These bounds and their analysis lead to a better understanding of clustering behavior under various implied connectivity structures behind the data and to new rates of convergence for centroid recovery. The new theoretical framework is based on random walks, which allow application of concentration inequalities related to random graph models, and formalizes the relationship between the clustering performance and the connectivity of the graph structures. Through the form of the bound and empirical results, we argue proper tuning of hyperparameters to convex clustering problems should also include tuning of input affinity weights.
Comments: 28 pages, 6 figures
Subjects: Machine Learning (stat.ML); Machine Learning (cs.LG)
Cite as: arXiv:2605.24673 [stat.ML]
  (or arXiv:2605.24673v1 [stat.ML] for this version)
  https://doi.org/10.48550/arXiv.2605.24673

arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Samuel Rosen [view email]
[v1] Sat, 23 May 2026 17:17:36 UTC (1,557 KB)