The Principal Axes Method for Constructive Induction

Abstract

The paper describes a novel method for constructive induction, called PRAX (Principal Axes). The underlying idea of the method is to determine descriptions of a class of certain basic concepts, and then use these descriptions as “principal axes” with which all other concepts can be described. Given examples of a new concept, the system determines a similarity matrix (SM) for that concept, that contains the average degree of similarity between the concept examples and the principal axes. These degrees of similarity are viewed as newly constructed attributes. To recognize an unknown concept instance, the method creates an SM for it, and then seeks the best matching similarity matrix of all known concepts. In experimental testing of the method on the problem of learning descriptions of a large number of visual textures, the PRAX method significantly outperformed the k-NN classifier often used for such problems. A very important result of this research is a demonstration that a symbolic learning method can be successfully applied to the domain of continuous attributes of low level vision in which nonsymbolic methods have been traditionally employed.