Comparison of two unsupervised learning algorithms

The binary decision element described by the decision rule depending upon weight vector w is a model of neuron examined in this paper. The environment of the element is described by some unknown, stationary distribution p(x). The input signals x[n] of the element appear in each step n independently in accordance with the distribution p(x). During an unsupervised learning process the weight vector w[n] is changed on the base of the input vector x[n]. In the paper there are regarded two self-learning algorithms which are stochastic approximation type. For both algorithms the same rule of past experiences neglecting or the rule of weight decrease has been introduced. The first algorithm differs from the other one by a rule of weight increase. It has been proved that only one of these algorithms always leads to the same decision rule in a given environment p(x).This work was done during stay of Dr. L. Bobrowski at the University of Salerno in the frame of Polish-Italian Agreement on Scientific Cooperation