RELATIONSHIP BETWEEN ORGANIZING CAPABILITY AND INFORMATION UTILIZED FOR SYSTEM ORGANIZATION

Summary This paper presents the fundamental properties of the typical parametric organizers for the supervised and the nonsupervised classification and makes clear the relationship between the organizing capability and the information which is utilized for the system organization. In the supervised case, the system performance is evaluated uniformly by means of the concept of the information processing capacity and the percent information processing capacity under the assumption that the pattern is distributed according to the multivariate normal distribution. The typical organizers considered here are (1) the minimum distance organizer, (2) the Bayes organizer, (3) the regression organizer, (4) the linear admissible organizer, (5) the multi-regression organizer, (6) the partial Bayes organizer, (7) the modified Fisher organizer and (8) the modified regression organizer. In the nonsupervised case, two basic organizing methods are considered. The one is the nonsupervised organizer by a stochastic approximation method, and the other is by the Karhunen-Loeve orthogonal system. For the first case, two basic algorithms are considered on the typical criterions. The one is the criterion to minimize the distance between the mean values of two categories, and the other is to minimize the average distance between the hyperplane and the sample patterns for each category. We also discuss the relationship between the organizing capability and the information which is utilized for its system organization. For the second case, in order to organize the system, number of trials are required utilizing the Karhunen-Loeve orthogonal system, but it is proved that there exists a dichotomy which converges to the Bayes solution by increasing the number of samples, if the mixture distribution is identifiable and some conditions are satisfied.