Variational Bayesian inference with Automatic Relevance Determination for Generative Topographic Mapping

Generative Topographic Mapping (GTM) is a nonlinear latent variable model introduced by Bishop et al. as a data visualization technique. In this paper, we focus on variational Bayesian inference for the GTM. The variational Bayesian GTM was first proposed by Olier et al. However, the GTM of Olier et al. uses a single regularization term and regularization parameter to avoid overfitting and therefore cannot locally control the degree of regularization. To overcome the problem, we propose the variational Bayesian inference with Automatic Relevance Determination (ARD) hierarchical prior for the GTM. The proposed model uses multiple regularization parameters and therefore can individually control the degree of regularization in each local area of the data space. Several experiments show that the proposed GTM provides better visualization than the conventional GTM approaches.