Constructing Generative Topographic Mapping by Variational Bayes with ARD Hierarchical Prior

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