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This paper illustrates the new structure of artificial neuron based on root-power mean (RPM) aggregation for quaternionic-valued signals and also presented an efficient learning process of neural networks with quaternionic-valued RPM neurons. 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 spectra of benchmark problem are considered to evaluate the performance of proposed quaternionic RPM neuron with ℍ-RPROP learning algorithm. [ABSTRACT FROM AUTHOR]

There are various high-dimensional engineering and scientific applications in communication, control, robotics, computer vision, biometrics, etc.; where researchers are facing predicament to fabricate an intelligent and robust neural system which can process higher dimensional information efficiently. In various literatures, the conventional neural networks based only on real valued, are tried to solve the problem associated with high-dimensional parameters, but these neural network structures possess high complexity and are very time consuming and weak to noise. These networks are also not able to learn magnitude and phase values simultaneously in space. The quaternion is the number, which possesses the magnitude in all four directions and phase information is embedded within it. This paper presents a learning machine with a quaternionic domain neural network that can finely process magnitude and phase information of high dimension data without any hassle. The learning and generalization capability of the proposed learning machine is performed through chaotic time series predictions (Lorenz system and Chua's circuit), 3D linear transformations, and 3D face recognition as benchmark problems, which demonstrate the significance of the work. [ABSTRACT FROM AUTHOR]