High-dimensional information processing through resilient propagation in quaternionic domain

Abstract This paper proposes a fast but effective machine learning technique for the high-dimensional information processing problems. A quaternion is the hyper-complex number in four dimensions which possesses four components in a single body with embedded phase information among their components. Thus, a neural network with quaternion as unit of information flow has ability to learn and generalize magnitude and argument of high-dimensional information simultaneously. The slow convergence and getting stuck into bad minima are the main drawbacks of the back-propagation learning algorithm; therefore learning technique with faster convergence is the demand of quaternionic neurocomputing. The basic issues of quaternionic back-propagation (ℍ-BP) algorithm have been combated by proposed resilient propagation algorithm in quaternionnic domain (ℍ-RPROP). The efficient and intelligent behavior of the proposed learning algorithm has been vindicated by the wide spectrum of benchmark problems. The simulations on different transformations demonstrate its ability to learn 3D motion, which is very desirable in viewing of objects through different orientations in many engineering applications. The critical thing is the training through mapping over straight line having a small number of points and eventually generalization over complicated geometrical structures (Sphere, Cylinder and Torus) possessing huge amount of point cloud data. The 3D and 4D time series prediction as benchmark applications are also taken into the account for the significant contribution of the proposed work. The substantial edge of the proposed algorithm is its quicker convergence with better approximation capability in high-dimensional problems.