A unified framework for hard and soft clustering with regularized optimal transport

arXiv:1711.04366v2 Announce Type: replace
Abstract: In this paper, we formulate the problem of inferring a Finite Mixture Model from discrete data as an optimal transport problem with entropic regularization of parameter $\lambda\geq 0$. Our method unifies hard and soft clustering, the Expectation-Maximization (EM) algorithm being exactly recovered for $\lambda=1$. The family of clustering algorithm we propose rely on the resolution of nonconvex problems using alternating minimization. We study the convergence property of our generalized $\lambda-$EM algorithms and show that each …

abstract algorithm arxiv clustering cs.lg data expectation-maximization framework lambda paper regularization stat.ml transport type