A modified learning algorithm for the multilayer neural network with multi-valued neurons based on the complex QR decomposition

In this paper, a modified learning algorithm for the multilayer neural network with the multi-valued neurons (MLMVN) is presented. The MLMVN, which is a member of complex-valued neural networks family, has already demonstrated a number of important advantages over other techniques. A modified learning algorithm for this network is based on the introduction of an acceleration step, performing by means of the complex QR decomposition and on the new approach to calculation of the output neurons errors: they are calculated as the differences between the corresponding desired outputs and actual values of the weighted sums. These modifications improve significantly the existing derivative-free backpropagation learning algorithm for the MLMVN in terms of learning speed. A modified learning algorithm requires two orders of magnitude lower number of training epochs and less time for its convergence when compared to the existing learning algorithm. Good performance is confirmed not only by the much quicker convergence of the learning algorithm, but also by the compatible or even higher classification/prediction accuracy, which is obtained by testing over some benchmarks (Mackey-Glass and Jenkins-Box time series) and over some satellite spectral data examined in a comparison test. Kewords— complex-valued neural networks, derivative-free learning, QR decomposition, time series prediction