Local versions of sum-of-norms clustering
Machine Learning
2024-07-16 v3 Statistics Theory
Machine Learning
Statistics Theory
Abstract
Sum-of-norms clustering is a convex optimization problem whose solution can be used for the clustering of multivariate data. We propose and study a localized version of this method, and show in particular that it can separate arbitrarily close balls in the stochastic ball model. More precisely, we prove a quantitative bound on the error incurred in the clustering of disjoint connected sets. Our bound is expressed in terms of the number of datapoints and the localization length of the functional.
Keywords
Cite
@article{arxiv.2109.09589,
title = {Local versions of sum-of-norms clustering},
author = {Alexander Dunlap and Jean-Christophe Mourrat},
journal= {arXiv preprint arXiv:2109.09589},
year = {2024}
}
Comments
20 pages, 2 figures, accepted version, to appear in SIAM J. Math. Data Sci