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Manifold Preserving Hierarchical Topic Models for Quantization and Approximation

Minje Kim, Paris Smaragdis
;
JMLR W&CP 28 (3) : 1373–1381, 2013

Abstract

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 mid-layer 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.

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