Extended Kalman filter learning algorithm for hyper-complex multilayer neural networks

A new type of multilayer perceptron (MLP), developed in quaternion algebra, has been used to perform hyper-complex nonlinear mappings and time series prediction employing a reduced network complexity with respect to conventional MLPs. The extended Kalman filter (EKF) technique has been used as an online algorithm to train MLP neural networks. This training technique significantly reduces the convergence and memory requirement compared with the standard backpropagation method. In this paper, a new learning algorithm, the hyper-complex EKF is derived for the hyper-complex MLP neural network. As an application, a short term prediction of a time-series generated from the hyperchaotic Saito circuit is considered