Recovery of a Mixture of Gaussians by Sum-of-Norms Clustering
Tao Jiang, Stephen Vavasis, Chen Wen Zhai.
Year: 2020, Volume: 21, Issue: 225, Pages: 1−16
Abstract
Sum-of-norms clustering is a method for assigning n points in Rd to K clusters, 1≤K≤n, using convex optimization. Recently, Panahi (2017) proved that sum-of-norms clustering is guaranteed to recover a mixture of Gaussians under the restriction that the number of samples is not too large. The purpose of this note is to lift this restriction, that is, show that sum-of-norms clustering can recover a mixture of Gaussians even as the number of samples tends to infinity. Our proof relies on an interesting characterization of clusters computed by sum-of-norms clustering that was developed inside a proof of the agglomeration conjecture by Chiquet et al. (2017). Because we believe this theorem has independent interest, we restate and reprove the Chiquet et al. (2017) result herein.