  We present a discriminative clustering approach in which the feature
representation can be learned from data and moreover leverage labeled data.
Representation learning can give a similarity-based clustering method the
ability to automatically adapt to an underlying, yet hidden, geometric
structure of the data. The proposed approach augments the DIFFRAC method with a
representation learning capability, using a gradient-based stochastic training
algorithm and an optimal transport algorithm with entropic regularization to
perform the cluster assignment step. The resulting method is evaluated on
several real datasets when varying the ratio of labeled data to unlabeled data
and thereby interpolating between the fully unsupervised regime and the fully
supervised regime. The experimental results suggest that the proposed method
can learn powerful feature representations even in the fully unsupervised
regime and can leverage even small amounts of labeled data to improve the
feature representations and to obtain better clusterings of complex datasets.
