GTM with latent variable dependent length-scale and variance

Generative Topographic Mapping (GTM) is a data visualization technique that uses a nonlinear topographically preserving mapping from latent to data space. Conventional GTM models can be interpreted as a probabilistic model using Gaussian process prior, and therefore the choice of covariance function in the Gaussian process prior has an important effect on the performance. However the conventional GTM models use a covariance function with a constant length-scale for the whole latent space, and therefore fail to adapt to variable smoothness in the nonlinear topographically preserving mapping. In this paper, we propose GTM with latent variable dependent length-scale (GTM-LDLV), which can adjust the smoothness in local areas of the latent space individually.