The extended piecewise quadratic neural network
We present a new neural network for detection and classification problems that is capable of creating spherical, elliptical, hyperbolic and linear decision surfaces. This new classifier is called the extended piecewise quadratic neural network (E-PQNN) and uses complex-valued weights and a square-law non-linearity. We prove that our simple E-PQNN architecture 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 optimizer. We present results obtained for a synthetic problem.
neural networks non-linear classifier quadratic forms pattern recognition