Unsupervised Classifiers, Mutual Information and 'Phantom Targets'

We derive criteria for training adaptive classifier networks to perform unsupervised data analysis. The first criterion turns a simple Gaussian classifier into a simple Gaussian mixture analyser. The second criterion, which is much more generally applicable, is based on mutual information. It simplifies to an intuitively reasonable difference between two entropy functions, one encouraging 'decisiveness,' the other 'fairness' to the alternative interpretations of the input. This 'firm but fair' criterion can be applied to any network that produces probability-type outputs, but it does not necessarily lead to useful behavior.