Performance Evaluation of Complex Valued Neural Networks Using Various Error Functions

The backpropagation algorithm in general employs quadratic error function. In fact, most of the problems that involve minimization employ the Quadratic error function. With alternative error functions the performance of the optimization scheme can be improved. The new error functions help in suppressing the ill-effects of the outliers and have shown good performance to noise. In this paper we have tried to evaluate and compare the relative performance of complex valued neural network using different error functions. During first simulation for complex XOR gate it is observed that some error functions like Absolute error, Cauchy error function can replace Quadratic error function. In the second simulation it is observed that for some error functions the performance of the complex valued neural network depends on the architecture of the network whereas with few other error functions convergence speed of the network is independent of architecture of the neural network. Keywords—Complex backpropagation algorithm, complex error functions, complex valued neural network, split activation function.

[1]  Yan Hui,et al.  A data extrapolation algorithm using a complex domain neural network , 1997 .

[2]  W. Rey.  Introduction to Robust and Quasi-Robust Statistical Methods , 1983 .

[3]  Tohru Nitta,et al.  An Extension of the Back-Propagation Algorithm to Complex Numbers , 1997, Neural Networks.

[4]  B. Widrow,et al.  The complex LMS algorithm , 1975, Proceedings of the IEEE.

[5]  Jianqiang Yi,et al.  Backpropagation based on the logarithmic error function and elimination of local minima , 1991, [Proceedings] 1991 IEEE International Joint Conference on Neural Networks.

[6]  Akira Hirose,et al.  Dynamics of fully complex-valued neural networks , 1992 .

[7]  Cris Koutsougeras,et al.  Complex domain backpropagation , 1992 .

[8]  Paul J. Werbos,et al.  An Empirical Test of New Forecasting Methods Derived from a Theory of Intelligence: The Prediction of Conflict in Latin America , 1978, IEEE Transactions on Systems, Man, and Cybernetics.

[9]  Clark C. Guest,et al.  Modification of backpropagation networks for complex-valued signal processing in frequency domain , 1990, 1990 IJCNN International Joint Conference on Neural Networks.

[10]  Philip E. Gill,et al.  Practical optimization , 1981 .

[11]  Jun Wang,et al.  Recurrent neural networks for solving systems of complex-valued linear equations , 1992 .

[12]  Y. Deville.  A neural implementation of complex activation functions for digital VLSI neural networks , 1993 .

[13]  Francesco Piazza,et al.  On the complex backpropagation algorithm , 1992, IEEE Trans. Signal Process..