On Self-Learning Systems

Abstract The fundamental problem on self-learning is discussed. The characteristics and the capability of two representative organizers obtained by the Karhunen-Loeve system and the stochastic approximation method are described and their relationship with Bayes' solution is discussed. The organization obtainable by the KL system is realized by calculating the difference of the features between the categories and by classifying the system so as to maximize this difference. This procedure is shown to be optimal. Further, the sufficient condition for this procedure to be the Bayes' solution is derived. For the organization attainable by the stochastic approximation method, two functional to be evaluated are introduced and the system is organized so as to minimize these functionals. The necessary and the sufficient conditions for these procedures to be Bayes' solution are obtained for the mixture of normal distributions with identical covariance matrices. The several simulations on a digital computer are perf...