On the learning machine in quaternionic domain and its application
by Sushil Kumar; Bipin Kumar Tripathi
International Journal of Advanced Intelligence Paradigms (IJAIP), Vol. 25, No. 1/2, 2023

Abstract: There are various high-dimensional engineering and scientific applications in communication, control, robotics, computer vision, biometrics, etc.; where researchers are facing problem to design an intelligent and robust neural system which can process higher dimensional information efficiently. In various literatures, the conventional real-valued neural networks are tried to solve the problem associated with high-dimensional parameters, but the required network structure possesses 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 generalisation capability of the proposed learning machine is presented through 3D linear transformations, 3D face recognition and chaotic time series predictions (Lorenz system and Chua's circuit) as benchmark problems, which demonstrate the significance of the work.

Online publication date: Thu, 11-May-2023

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