We suppose that each of the patterns that we want to classify can be
completely described by an N-dimensional random variable 
. Based on
the observation of one instance of our task is to assign the
underlying pattern to one of the classes 
. We are therefore interested in finding a function
representing a so-called decision rule. For our purposes this function shall be deterministic. Since, in most cases, it is impossible or insufficient to write down a simple decision rule in closed form, we are investigating methods for ``learning'' the decision rule from a set of training examples for which the actual class is known. In other words, our problem is to find a mechanism for supervised learning of a decision rule.