Enregistré dans:
Détails bibliographiques
Auteurs principaux: Diebold, Jean-Frédéric, Papadakis, Nicolas, Dessein, Arnaud, Deledalle, Charles-Alban
Format: Preprint
Publié: 2017
Sujets:
Accès en ligne:https://arxiv.org/abs/1711.04366
Tags: Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
_version_ 1866929267791626240
author Diebold, Jean-Frédéric
Papadakis, Nicolas
Dessein, Arnaud
Deledalle, Charles-Alban
author_facet Diebold, Jean-Frédéric
Papadakis, Nicolas
Dessein, Arnaud
Deledalle, Charles-Alban
contents 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 $λ\geq 0$. 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 $λ\to 0$ for classification.
format Preprint
id arxiv_https___arxiv_org_abs_1711_04366
institution arXiv
publishDate 2017
record_format arxiv
spellingShingle A unified framework for hard and soft clustering with regularized optimal transport
Diebold, Jean-Frédéric
Papadakis, Nicolas
Dessein, Arnaud
Deledalle, Charles-Alban
Machine Learning
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 $λ\geq 0$. 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 $λ\to 0$ for classification.
title A unified framework for hard and soft clustering with regularized optimal transport
topic Machine Learning
url https://arxiv.org/abs/1711.04366