GTM - THE GENERATIVE TOPOGRAPHIC MAPPING

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 ba sed on a linear transformation between the latent space and the data s pace. In this article, we introduce a form of nonlinear latent variabl e model tailed the generative topographic mapping, for which the param eters of the model can be determined using the expectation-maximizatio n algorithm. GTM provides a principled alternative to the widely used self-organizing map (SOM) of Kohonen (1982) and overcomes most of the significant limitations of the SOM. We demonstrate the performance of the GTM algorithm on a toy problem and on simulated data from now diag nostics for a multiphase oil pipeline.