Mathematical Study of Conceptualization in N-Dimensional Space
Masanobu Ohtsuki, Atsushi Minato, Satoru Ozawa · Forma · 2000
A concept of a thing is characterized by a set of suitable parameters. It can be approximately represented as a rectangle in n-dimensional space. The process of obtaining the concept from a number of observations produces a series of in n- dimensional space, where each sample point has a value of 1 or 0 depending upon whether the sample suits with the concept or not. The accuracy of guessing n-dimensional rectangle from sample points is related to the way of generating samples. The HIS (Half Interval Search) method is proposed to produce the sample points. It has been shown that it is an efficient method and the expected error in the determination of the concept is O(1/m), where m is the number of sample points. This method is successfully used for identification of a smiling face in a cartoon figure.