Local versions of sum-of-norms clustering

TL;DR

This paper introduces a localized variant of sum-of-norms clustering, demonstrating its ability to effectively separate closely situated data clusters and providing quantitative error bounds based on data and localization parameters.

Contribution

It proposes a new localized sum-of-norms clustering method and establishes theoretical guarantees for its performance in separating close data clusters.

Findings

Can separate arbitrarily close clusters in the stochastic ball model

Provides explicit error bounds related to data size and localization length

Enhances understanding of convex clustering methods

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.