Co-clustering through Optimal Transport

Charlotte Laclau, Ievgen Redko, Basarab Matei, Younès Bennani, Vincent Brault
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:1955-1964, 2017.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v70-laclau17a, title = {Co-clustering through Optimal Transport}, author = {Charlotte Laclau and Ievgen Redko and Basarab Matei and Youn{\`e}s Bennani and Vincent Brault}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, pages = {1955--1964}, year = {2017}, editor = {Precup, Doina and Teh, Yee Whye}, volume = {70}, series = {Proceedings of Machine Learning Research}, month = {06--11 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v70/laclau17a/laclau17a.pdf}, url = {https://proceedings.mlr.press/v70/laclau17a.html}, 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.} }
Endnote
%0 Conference Paper %T Co-clustering through Optimal Transport %A Charlotte Laclau %A Ievgen Redko %A Basarab Matei %A Younès Bennani %A Vincent Brault %B Proceedings of the 34th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Doina Precup %E Yee Whye Teh %F pmlr-v70-laclau17a %I PMLR %P 1955--1964 %U https://proceedings.mlr.press/v70/laclau17a.html %V 70 %X 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.
APA
Laclau, C., Redko, I., Matei, B., Bennani, Y. & Brault, V.. (2017). Co-clustering through Optimal Transport. Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research 70:1955-1964 Available from https://proceedings.mlr.press/v70/laclau17a.html.

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