Generative topographic mapping as a constrained mixture of student t-distributions: theoretical developments

The Generative Topographic Mapping (GTM: Bishop et al. 1998a), a non-linear latent variable model, was originally defined as constrained mixture of Gaussians. Gaussian mixture models are known to lack robustness in the presence of outlier observations in the data sample, and multivariate Student t-distributions have recently been put forward as a more robust alternative to deal with continuous data in this context.Postprint (published version