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

• URL: http://arxiv.org/abs/1711.04366v2
• Date: Thu, 7 Mar 2024 20:43:31 GMT
• Title: A unified framework for hard and soft clustering with regularized optimal transport
• Authors: Jean-Frédéric Diebold, Nicolas Papadakis, Arnaud Dessein, Charles-Alban Deledalle,
• Abstract summary: In this paper, we formulate the problem of inferring a Finitelamblambdageq 0 from discrete data as an optimal transport problem with entropic regularization.
• Score: 5.715859759904031
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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 $\lambda>1$ to improve the inference performance and $\lambda\to 0$ for classification.

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