Co-clustering through Optimal Transport
This addresses the problem of unsupervised co-clustering for data analysis, offering an incremental improvement with theoretical justification and experimental validation.
The paper tackles co-clustering by proposing a method based on entropy-regularized optimal transport to estimate a joint probability density and factorize it for partitions, resulting in a fast and accurate algorithm that automatically determines the number of clusters.
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.