Missing data imputation through GTM as a mixture of tt-distributions

The Generative Topographic Mapping (GTM) was originally conceived as a probabilistic alternative to the well-known, neural network-inspired, Self-Organizing Maps. The GTM can also be interpreted as a constrained mixture of distribution models. In recent years, much attention has been directed towards Student tt-distributions as an alternative to Gaussians in mixture models due to their robustness towards outliers. In this paper, the GTM is redefined as a constrained mixture of tt-distributions: the tt-GTM, and the Expectation–Maximization algorithm that is used to fit the model to the data is modified to carry out missing data imputation. Several experiments show that the tt-GTM successfully detects outliers, while minimizing their impact on the estimation of the model parameters. It is also shown that the tt-GTM provides an overall more accurate imputation of missing values than the standard Gaussian GTM.