Single-layered complex-valued neural networks and their ensembles for real-valued classification problems

This paper presents a complex-valued neuron (CVN) model for real-valued classification problems incorporating a new activation function. The activation function maps complex-valued net-inputs (sum of weighted inputs) of a neuron into bounded real-values, and its role is to divide the net-input space into different regions for different classes. A gradient-descent learning rule has been derived to train the CVN. Such a CVN is able to solve all possible two-input Boolean functions. For further investigation, single layered complex-valued neural networks (Le. without hidden units) are applied on the real-world multi-class classification problems. The results are comparable to the conventional multilayer real-valued neural networks. It is also shown that the performance can be improved further by using their ensembles. Negative correlation learning (NCL) algorithm has been used to create the ensembles. Since NCL is a gradient-descent based algorithm, the proposed activation function is well suited for it.