A convergent algorithm for a cascade network of multiplexed dual output discrete perceptrons for linearly nonseparable classification

Abstract

In this paper a new discrete perceptron model is introduced. The model forms a cascade structure and it is capable of realizing an arbitrary classification task designed by a constructive learning algorithm. The main idea is to copy a discrete perceptron neuron's output to have a complementary dual output for the neuron, and then to select, by using a multiplexer, the true output, which might be 0 or 1 depending on the given input. Hence, the problem of realization of the desired output is transformed into the realization of the selector signal of the multiplexer. In the next step, the selector signal is taken as the desired output signal for the remaining part of the network. The repeated applications of the procedure render the problem into a linearly separable one and eliminate the necessity of using the selector signal in the last step of the algorithm. The proposed modification to the discrete perceptron brings universality with the expense of getting just a slight modification in hardware implementation.