The novel aggregation function-based neuron models in complex domain

Abstract

The computational power of a neuron lies in the spatial grouping of synapses belonging to any dendrite tree. Attempts to give a mathematical representation to the grouping process of synapses continue to be a fascinating field of work for researchers in the neural network community. In the literature, we generally find neuron models that comprise of summation, radial basis or product aggregation function, as basic unit of feed-forward multilayer neural network. All these models and their corresponding networks have their own merits and demerits. The MLP constructs global approximation to input–output mapping, while a RBF network, using exponentially decaying localized non-linearity, constructs local approximation to input–output mapping. In this paper, we propose two compensatory type novel aggregation functions for artificial neurons. They produce net potential as linear or non-linear composition of basic summation and radial basis operations over a set of input signals. The neuron models based on these aggregation functions ensure faster convergence, better training and prediction accuracy. The learning and generalization capabilities of these neurons have been tested over various classification and functional mapping problems. These neurons have also shown excellent generalization ability over the two-dimensional transformations.