The topographic product of experts

We create a new form of topographic map which is based on a nonlinear mapping of a space of latent points. The mapping of these latent points into data space creates centres which are equivalent to those of the standard SOM. We relate this mapping to the Generative Topographic Mapping, GTM. We then show that it is rather simple and computationally inexpensive to grow one of these maps and that a probabilistic interpretation of these maps facilitates our investigation of alternative algorithms.