Deep $k$-Means: Jointly clustering with $k$-Means and learning\n representations

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