Title: Parameter Estimation in Finite Mixture Models by Regularized Optimal Transport: A Unified Framework for Hard and Soft Clustering,
Abstract: In this short paper, we formulate parameter estimation for finite mixture
models in the context of discrete optimal transportation with convex
regularization. The proposed framework unifies hard and soft clustering methods
for general mixture models. It also generalizes the celebrated
$k$\nobreakdash-means and expectation-maximization algorithms in relation to
associated Bregman divergences when applied to exponential family mixture
models.