  Any clustering algorithm must synchronously learn to model the clusters and
allocate data to those clusters in the absence of labels. Mixture model-based
methods model clusters with pre-defined statistical distributions and allocate
data to those clusters based on the cluster likelihoods. They iteratively
refine those distribution parameters and member assignments following the
Expectation-Maximization (EM) algorithm. However, the cluster representability
of such hand-designed distributions that employ a limited amount of parameters
is not adequate for most real-world clustering tasks. In this paper, we realize
mixture model-based clustering with a neural network where the final layer
neurons, with the aid of an additional transformation, approximate cluster
distribution outputs. The network parameters pose as the parameters of those
distributions. The result is an elegant, much-generalized representation of
clusters than a restricted mixture of hand-designed distributions. We train the
network end-to-end via batch-wise EM iterations where the forward pass acts as
the E-step and the backward pass acts as the M-step. In image clustering, the
mixture-based EM objective can be used as the clustering objective along with
existing representation learning methods. In particular, we show that when
mixture-EM optimization is fused with consistency optimization, it improves the
sole consistency optimization performance in clustering. Our trained networks
outperform single-stage deep clustering methods that still depend on k-means,
with unsupervised classification accuracy of 63.8% in STL10, 58% in CIFAR10,
25.9% in CIFAR100, and 98.9% in MNIST.
