On the learning machine with quaternionic domain neural network and its high-dimensional applications

摘要

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.