On the benefits for model regularization of a variational formulation of GTM

Generative topographic mapping (GTM) is a manifold learning model for the simultaneous visualization and clustering of multivariate data. It was originally formulated as a constrained mixture of distributions, for which the adaptive parameters were determined by maximum likelihood (ML), using the expectation-maximization (EM) algorithm. In this formulation, GTM is prone to data overfitting unless a regularization mechanism is included. The theoretical principles of variational GTM, an approximate method that provides a full Bayesian treatment to a Gaussian process (GP)-based variation of the GTM, were recently introduced as alternative way to control data overfitting. In this paper we assess in some detail the generalization capabilities of Variational GTM and compare them with those of alternative regularization approaches in terms of test log-likelihood, using several artificial and real datasets.