Steady-State Behavior of a Nonsupervised Learning Algorithm for Multicategory Pattern Classification

A nonsupervised learning algorithm for multicategory pattern classification is presented, and its steady-state behavior is investigated by means of analysis and simulation. The algorithm assigns each pattern in an input sequence x(t) to one of the M possible categories by comparing the M values wi(t)´ x(t), i = 1,2,...,M, where wi(t)are variable weight vectors adjusted according to a differential-equation type of rule. The algorithm minimizes a certain form of criterion function. Analytical techniques are developed for finding the steady-state solutions of the differential equation and for determining the stability of each solution found. By applying the techniques, the steady-state behavior of the algorithm to three types of patterns is analyzed in detail. It is shown that although the algorithm does not necessarily yield a unique solution every solution yielded is associated with a reasonable Classification such that one cluster or some adjacent clusters in the pattern distribution correspond to one category. Even if the total number of clusters in the distribution is smaller than M, no cluster is divided between two categories. Converging to the origin, unnecessary weight vectors vanish in the steady state. These results are verified by some digital computer simulations.