English

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