A Comprehensive Review on the Advancement of High-Dimensional Neural Networks in Quaternionic Domain with Relevant Applications

The neurocomputing communities have focused much interest on quaternionic-valued neural networks (QVNNs) due to the natural extension in quaternionic signals, learning of inter and spatial relationships between the features, and remarkable improvement against real-valued neural networks (RVNNs) and complex-valued neural networks (CVNNs). The excellent learning capability of QVNN inspired the researchers working on various applications in image processing, signal processing, computer vision, and robotic control system. Apart from its applications, many researchers have proposed new structures of quaternionic neurons and extended the architecture of QVNN for specific applications containing high-dimensional information. These networks have revealed their performance with a lesser number of parameters over conventional RVNNs. This paper focuses on past and recent studies of simple and deep QVNNs architectures and their applications. This paper provides the future directions to prospective researchers to establish new architectures and to extend the existing architecture of high-dimensional neural networks with the help of quaternion, octonion, or sedenion for appropriate applications.