A fuzzy threshold max-product unit, with learning algorithm, for classification of pattern vectors

Abstract

Proposes a max-product threshold unit (maptu) that, like a single perceptron, can perform dichotomous classifications of pattern vectors. Maptu classifies a pattern vector, x, by determining whether x max-prod w is less than 0.5 or greater than 0.5. Here w, consisting of non-negative values, is referred to as the weight vector. As part of training w is found by setting it equal to c* 0.5/max X/sup -/. X/sup -/ is the matrix whose rows are the training patterns belonging to class-. Maximization is done within the columns of X/sup -/. Since (x max-prod w<0.5) vs. (x max-prod w>0.5) is not symmetrical because the former is much more restrictive than the latter a satisfiability factor based on X/sup -/ and X/sup +/ is calculated to determine which set of training data should be labeled class-and which should be labeled class/sup +/. Let X/sup +/ denote the matrix whose rows are the training patterns belonging to class/sup +/. The only iteration is involved in finding c by trying values greater than 0 near 1. The method is tried with success on 4 different sets of data. Results obtained by other methods in classification of this data is used for comparison to the method using maptu.