Fixed point rules for heteroscedastic Gaussian kernel-based topographic map formation

Abstract

We develop a number of fixed point rules for training homogeneous, heteroscedastic but otherwise radially-symmetric Gaussian kernel-based topographic maps. We extend the batch map algorithm to the heteroscedastic case and introduce two candidates of fixed point rules for which the end-states, i.e., after the neighborhood range has vanished, are identical to the maximum likelihood Gaussian mixture modeling case. We compare their performance for clustering a number of real world data sets.