PP: Unsupervised deep embedding for clustering analysis

Problem: unsupervised clustering

represent data in feature space; learn a non-linear mapping from data space X to feature space Z. 

Problem formulation: cluster a set of n points into k clusters, each represented by a centroid u_j.

 Instead of clustering directly in the data space X, we propose to first transform the data with a nonlinear mapping fθ : X → Z, where θ are learnable parameters and Z is the latent feature space.