A Unified Framework for Hard and Soft Clustering with Regularized Optimal Transport
Abstract: We formulate the inference of a finite mixture model from discrete data as an optimal transport problem with entropic regularization of parameter <tex>$\lambda\geq 0$</tex>. Our method unifies hard and soft clustering, the Expectation-Maximization (EM) algorithm being exactly recovered for <tex>$\lambda=1$</tex>. The family of clustering algorithm we propose relies on the resolution of nonconvex problems using alternating minimization. We study the convergence property of our generalized <tex>$\lambda-\text{EM}$</tex> algorithms and show that each algorithmic step has a closed form solution when inferring finite mixture models of exponential families. Experiments highlight the benefits of taking a parameter <tex>$\lambda > 1$</tex> to improve the inference performance and <tex>$\lambda\rightarrow 0$</tex> for classification.
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