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Co-clustering through Optimal Transport

Charlotte Laclau 1 Ievgen Redko 2 Basarab Matei 1 Younès Bennani 1 Vincent Brault 3
2 Images et Modèles
CREATIS - Centre de Recherche en Acquisition et Traitement de l'Image pour la Santé
3 SVH - Statistique pour le Vivant et l’Homme
LJK - Laboratoire Jean Kuntzmann
Abstract : In this paper, we present a novel method for co-clustering, an unsupervised learning approach that aims at discovering homogeneous groups of data instances and features by grouping them simultaneously. The proposed method uses the entropy regularized optimal transport between empirical measures defined on data instances and features in order to obtain an estimated joint probability density function represented by the optimal coupling matrix. This matrix is further factorized to obtain the induced row and columns partitions using multiscale representations approach. To justify our method theoretically, we show how the solution of the regularized optimal transport can be seen from the variational inference perspective thus motivating its use for co-clustering. The algorithm derived for the proposed method and its kernelized version based on the notion of Gromov-Wasserstein distance are fast, accurate and can determine automatically the number of both row and column clusters. These features are vividly demonstrated through extensive experimental evaluations.
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https://hal.archives-ouvertes.fr/hal-01539101
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Submitted on : Wednesday, June 14, 2017 - 2:08:43 PM
Last modification on : Friday, November 20, 2020 - 9:24:02 AM
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  • HAL Id : hal-01539101, version 1
  • ARXIV : 1705.06189

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Charlotte Laclau, Ievgen Redko, Basarab Matei, Younès Bennani, Vincent Brault. Co-clustering through Optimal Transport. 34th International Conference on Machine Learning, Aug 2017, Sydney, Australia. pp.1955-1964. ⟨hal-01539101⟩

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