Multivariate Student-tt self-organizing maps

The original Kohonen’s Self-Organizing Map model has been extended by several authors to incorporate an underlying probability distribution. These proposals assume mixtures of Gaussian probability densities. Here we present a new self-organizing model which is based on a mixture of multivariate Student-tt components. This improves the robustness of the map against outliers, while it includes the Gaussians as a limit case. It is based on the stochastic approximation framework. The ‘degrees of freedom’ parameter for each mixture component is estimated within the learning procedure. Hence it does not need to be tuned manually. Experimental results are presented to show the behavior of our proposal in presence of outliers, and its performance in adaptive filtering and classification problems.