Deep clustering with concrete k-means.

We address the problem of simultaneously learning a k-means clustering and deep feature representation from unlabelled data, which is of interest due to the potential for deep k-means to outperform traditional two-step feature extraction and shallow clustering strategies. We achieve this by developing a gradient estimator for the non-differentiable k-means objective via the Gumbel-Softmax reparameterisation trick. In contrast to previous attempts at deep clustering, our concrete k-means model can be optimised with respect to the canonical k-means objective and is easily trained end-to-end without resorting to time consuming alternating optimisation techniques. We demonstrate the efficacy of our method on standard clustering benchmarks.