A Topography-Preserving Latent Variable Model with Learning Metrics

Abstract

We introduce a new mapping model from a latent grid to the input space. The mapping preserves the topography but measures local distances in terms of auxiliary data that implicitly conveys information about the relevance or importance of local directions in the primary data space. Soft clusters corresponding to the map grid locations are defined into the primary data space, and a distortion measure is minimized for paired samples of primary and auxiliary data. The Kullback-Leibler divergence-based distortion is measured between the conditional distributions of the auxiliary data given the primary data, and the model is optimized with stochastic approximation yielding an algorithm that resembles the Self-Organizing Map, but in which distances are computed by taking into account the (local) relevance of directions.