The generalized product neuron model in complex domain

Abstract

This paper proposes a complex valued generalized product neuron (GPN) which tries to incorporate polynomial structure in the aggregation of inputs. The advantage of using this model is to bring in the non-linearity in aggregation function by taking a product of linear terms in each dimension of the input space. This aggregation function has the ability to capture higher-order correlations in the input data. Such neurons are capable of learning any problem irrespective of whether the multi dimensional data is linearly separable or not which resembles higher order neurons. But these neurons do not have combinatorial increase of the number of weights in the dimensions of inputs as higher order neurons. The learning and generalization capabilities of proposed neuron are demonstrated through variety of problems. It has been shown that some benchmark problems can be solved with single GPN only without hidden layer. © 2009 Springer Berlin Heidelberg.