Latent Beta Topographic Mapping

Abstract

This paper describes Latent Beta Topographic Mapping (LBTM), a generative probability model for non linear dimensionality reduction and density estimation. LBTM is based on Generative Topographic Mapping (GTM) and hence inherits its ability to map complex non linear manifolds. However, the GTM is limited in its ability to reliably estimate sophisticated densities on the manifold. This paper explores the possibilities of learning a probability distribution for the data on the lower dimensional latent space. Learning a distribution helps not only in density estimation but also in maintaining topographic structure. In addition, LBTM provides useful methods for sampling, inference and visualization of high dimensional data. Experimental results indicate that LBTM can reliably learn the structure and distribution of the data and is competitive with existing methods for dimensionality reduction and density estimation.