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 uj.

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.

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