THE EXTENDED PIECEWISE QUADRATIC NEURAL-NETWORK

We present a new neural network for detection and classification probl ems that is capable of creating spherical, elliptical, hyperbolic and linear decision surfaces. This new classifier is called the extended p iecewise quadratic neural network (E-PQNN) and uses complex-valued wei ghts and a square-law non-linearity. We prove that our simple E-PQNN a rchitecture is able to generate piecewise quadratic decision surfaces of arbitrary rank and we develop new methods for selecting the number of hidden-layer neurons in the E-PQNN. The weights are optimized using a modified perceptron error criterion and a conjugate gradient optimi zer. We present results obtained for a synthetic problem. (C) 1998 Els evier Science Ltd. All rights reserved.