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 significantly improve 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 with 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.
The use of computer based tools in electrical engineering courses should be always accompanied with the possibility to gain an insight into the circuit properties. This can be achieved by using a computer program which combines symbolic and numerical simulation capabilities. This approach in providing students of automatic analysis tools is more significant and complete. Therefore the program SAPWIN has been developed by the authors. This program includes the capability of generating the complete or approximate symbolic (fully or partially) output expressions of analog linear circuits and their graphical manipulation. In addition, it permits to obtain Spice netlist of a circuit, in order to work in a complete, selfsufficient environment, useful for both teachers and students. The program can be used "as is," like an useful tool during basic electrical sciences or network theory lessons, or like a starting platform on which to develop further application that requires symbolic formulas, eventually directly operating on the program code. The positive outcome of the first release of Sapwin, here presented, urged us to work on a completely renewed one, which will be ready as soon as possible. Antonio Luchetta (M'96) received the degree in Electronics Engineering from University of Florence, Italy, in 1993. He is a Researcher in the Department of Engineering and Environmental Physics at the University of Basilicata, Italy, where he also teaches electrical sciences. His research interests include software and algorithms for electric network simulation, neural network application to forecasting and control problem, elaboration of meteorological data. He is Member of IEEE and AEI.
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