  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 of 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 alternating optimisation. We demonstrate the efficacy of our
method on standard clustering benchmarks.
