Citation:
Jiang, T. , Vavasis, S. , & Zhai., C. W. . (2020). Recovery of a mixture of Gaussians by sum-of-norms clustering. Journal of Machine Learning Research, 21(225), 1-16. Retrieved from https://jmlr.org/papers/volume21/19-218/19-218.pdf
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 et al. (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.
Notes:
Arxiv link: http://arxiv.org/abs/1902.07137
