Manifold Preserving Hierarchical Topic Models for Quantization and Approximation

We present two complementary topic models to address the analysis of mixture data lying on manifolds. First, we propose a quantization method with an additional midlayer latent variable, which selects only data points that best preserve the manifold structure of the input data. In order to address the case of modeling all the in-between parts of that manifold using this reduced representation of the input, we introduce a new model that provides a manifold-aware interpolation method. We demonstrate the advantages of these models with experiments on the hand-written digit recognition and the speech source separation tasks.