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

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 λ≥ 0. Our method unifies hard and soft clustering, the Expectation-Maximization (EM) algorithm being exactly recovered for λ=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 λ-EM algorithms and show that each step in the minimization process has a closed form solution when inferring finite mixture models of exponential families. Experiments highlight the benefits of taking a parameter λ>1 to improve the inference performance and λ→ 0 for classification.