A Design Theory of Recognition Functions in Self-Organizing Systems

An analytical method of designing recognition functions in self-organizing systems is discussed in this paper. A mathematical model is defined which embodies recognition and learning processes based on past experiences. The ``desired function'' is introduced as the most faithful expression of recognition functions based on past experiences, and it is shown how to design the recognition function whose mean-square error from the desired function is minimized. The desired function makes it possible to utilize the orthonormal relationship between certain functions of inputs, and this gives a very simple design procedure for recognition functions. Also, since the desired function is a probability function of past experiences, the problems of learning and education can be discussed on a quantitative basis. Two concepts, forced education and statistical classification, are used in combination with the minimization technique of the mean-square error, and this gives a simple design procedure to improve the approximation abilities. The approximation abilities of linear recognition functions are studied in this paper for all linearly separable Boolean functions with two through six inputs.