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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2017
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/1711.04366 |
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| _version_ | 1866929267791626240 |
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| 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 |