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

摘要

The complex-valued nonlinear discriminant function (CNDF) proposed in the paper is based on a phi-function system which is obtained by generalizing the finite Walsh function to the case of many-valued variables. It can yield hypercurved decision surfaces. The recognition system with the CNDF has the following desired features: It can recognize not only binary patterns but also many-valued ones. The construction of the CNDF from training patterns requires only a simple calculation with no storage and no iteration for training patterns. A modification of the system due to new training patterns and/or an adaptive construction are also easily possible. The CNDF's assumption for pattern classes is clarified by the notion of the complexity between pattern classes.