Construction of a Complex-Valued Nonlinear Discriminant Function for Pattern Recognition

A method for constructing a new type of nonlinear discriminant function is proposed, and the capability is evaluated by computer simulation. As the orthogonal basis for this function, a ¿-function system is used that is obtained by generalizing the finite Walsh functions to the case of many-valued variables. The discriminant function discussed has the following desired features. It can deal with not only binary patterns, but also many-valued ones. The determination of a weighting vector requires neither storage nor iteration for training patterns. A notion of complexity between pattern classes is introduced to make clear the requirement of the present system for the structure of a pattern space. Examples of separation boundaries for 2-component-pattern classes demonstrate that the discriminant function has a high ability of generalization for new input patterns. The result of recognition experiments for artificial patterns indicates that for various values of the number of pattern components, the number of values taken by a component, and the complexity of pattern classes, the proposed system has sufficient rates of classification with a relatively small number of training patterns.