Local versions of sum-of-norms clustering

Alexander Dunlap , Jean-Christophe Mourrat (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

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.

Domaines: Apprentissage [cs.LG]

Alexander Dunlap, Jean-Christophe Mourrat. Local versions of sum-of-norms clustering. SIAM Journal on Mathematics of Data Science, 2022, 4 (4), pp.1250-1271. ⟨10.1137/21M1448732⟩. ⟨hal-03469585⟩