GTM: The Generative Topographic Mapping

TLDR

Latent variable models express data density in a lower‑dimensional latent space, exemplified by linear factor analysis. The article introduces the generative topographic mapping, a nonlinear latent variable model whose parameters are estimated via expectation‑maximization. The GTM algorithm is trained with expectation‑maximization and evaluated on a toy dataset and simulated multiphase oil pipeline flow diagnostics. GTM offers a principled alternative to Kohonen’s self‑organizing map, overcoming most of its major limitations.

Abstract

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 transformation between the latent space and the data space. In this article, we introduce a form of nonlinear latent variable model called the generative topographic mapping, for which the parameters of the model can be determined using the expectation-maximization 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 flow diagnostics for a multiphase oil pipeline.