A CLASSIFIER NEURAL-NET WITH COMPLEX-VALUED WEIGHTS AND SQUARE-LAW NONLINEARITIES

A new pattern recognition classifier neural net (NN) is described that uses complex-valued weights and square-law nonlinearities. We shaw that these weights and nonlinearities inherently produce higher-order decision surfaces and thus we expect better classification performance (P-C). We refer to this as the piecewise hyperquadratic neural net (PQNN) because each hidden layer neuron inherently provides a hyperquadratic decision surface and the combination of neurons provides piecewise hyperquadratic decision surfaces. We detail the learning algorithm for this NN and provide initial results on synthetic data showing its advantages over the back propagation and other NNs. We also note a new technique to provide improved classification results when there are significantly different numbers of samples per class.