  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.
