A Fuzzy Threshold Max-Product Unit, with Learning Algorithm, for Classification of Pattern Vectors

Roelof K. Brouwer

This paper 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-. X- is the matrix whose rows are the training patterns belonging to class -. Maximization is done within the columns of X-. 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- and X+ is calculated to determine which set of training data should be labeled class - and which should be labeled class +. Let X+ denote the matrix whose rows are the training patterns belonging to class +. The only iteration is involved in finding c by trying values greater than 0 near 1. The method is tried with success on four different sets of data. Results obtained by other methods in classification of this data are used for comparison to the method using maptu.

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