Levenberg-Marquardt Learning Algorithm for Quaternion-Valued Neural Networks

In this paper, we present the deduction of the Levenberg-Marquardt algorithm for training quaternion-valued feedforward neural networks, using the framework of the HR calculus. Its performances in the real-and complex-valued cases lead to the idea of extending it to the quaternion domain, also. The proposed method is exemplified on time series prediction applications, showing a significant improvement over the quaternion gradient descent algorithm.