GTM: The Generative Topographic Mapping

Accepted for publication in Neural Computation. Latent variable models represent the probability density of data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. A familiar example is factor analysis which is based on a linear transformations between the latent space and the data space. In this paper we introduce a form of non-linear latent variable model called the Generative Topographic Mapping for which the parameters of the model can be determined using the EM algorithm. GTM provides a principled alternative to the widely used Self-OrganizingMap (SOM) of Kohonen (1982), and overcomes most of the signicant limitations of the SOM. We demonstrate the performance of the GTM algorithm on a toy problem and on simulated data from ow diagnostics for a multi-phase oil pipeline. GTM: The Generative Topographic Mapping 2