  Most learning approaches treat dimensionality reduction (DR) and clustering
separately (i.e., sequentially), but recent research has shown that optimizing
the two tasks jointly can substantially improve the performance of both. The
premise behind the latter genre is that the data samples are obtained via
linear transformation of latent representations that are easy to cluster; but
in practice, the transformation from the latent space to the data can be more
complicated. In this work, we assume that this transformation is an unknown and
possibly nonlinear function. To recover the `clustering-friendly' latent
representations and to better cluster the data, we propose a joint DR and
K-means clustering approach in which DR is accomplished via learning a deep
neural network (DNN). The motivation is to keep the advantages of jointly
optimizing the two tasks, while exploiting the deep neural network's ability to
approximate any nonlinear function. This way, the proposed approach can work
well for a broad class of generative models. Towards this end, we carefully
design the DNN structure and the associated joint optimization criterion, and
propose an effective and scalable algorithm to handle the formulated
optimization problem. Experiments using different real datasets are employed to
showcase the effectiveness of the proposed approach.
