  We study in this paper the problem of jointly clustering and learning
representations. As several previous studies have shown, learning
representations that are both faithful to the data to be clustered and adapted
to the clustering algorithm can lead to better clustering performance, all the
more so that the two tasks are performed jointly. We propose here such an
approach for $k$-Means clustering based on a continuous reparametrization of
the objective function that leads to a truly joint solution. The behavior of
our approach is illustrated on various datasets showing its efficacy in
learning representations for objects while clustering them.
