On the Root-Power Mean Aggregation Based Neuron in Quaternionic Domain

Abstract

This paper illustrates the new structure of artificial neuron based on root-power means (RPM) for quaternionic-valued signals and also presented an efficient learning process of neural networks with quaternionic-valued root-power means neurons (ℍ-RPMN). The main aim of this neuron is to present the potential capability of a nonlinear aggregation operation on the quaternionic-valued signals in neuron cell. A wide spectrum of aggregation ability of RPM in between minima and maxima has a beautiful property of changing its degree of compensation in the natural way which emulates the various existing neuron models as its special cases. Further, the quaternionic resilient propagation algorithm (ℍ-RPROP) with error-dependent weight backtracking step significantly accelerates the training speed and exhibits better approximation accuracy. The wide spectrums of benchmark problems are considered to evaluate the performance of proposed quaternionic rootpower mean neuron with ℍ-RPROP learning algorithm.