Learning Algorithms for Quaternion-Valued Neural Networks

This paper presents the deduction of the enhanced gradient descent, conjugate gradient, scaled conjugate gradient, quasi-Newton, and Levenberg-Marquardt methods for training quaternion-valued feedforward neural networks, using the framework of the HR calculus. The performances of these algorithms in the real- and complex-valued cases led to the idea of extending them to the quaternion domain, also. Experiments done using the proposed training methods on time series prediction applications showed a significant performance improvement over the quaternion gradient descent algorithm.