A modified error backpropagation algorithm for complex-value neural networks

The complex-valued backpropagation algorithm has been widely used in fields of dealing with telecommunications, speech recognition and image processing with Fourier transformation. However, the local minima problem usually occurs in the process of learning. To solve this problem and to speed up the learning process, we propose a modified error function by adding a term to the conventional error function, which is corresponding to the hidden layer error. The simulation results show that the proposed algorithm is capable of preventing the learning from sticking into the local minima and of speeding up the learning.

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

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

[3]  Charles B. Owen,et al.  Application of simulated annealing to the backpropagation model improves convergence , 1993, Defense, Security, and Sensing.

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

[5]  Tohru Nitta,et al.  Solving the XOR problem and the detection of symmetry using a single complex-valued neuron , 2003, Neural Networks.

[6]  Werner von Seelen,et al.  On unlearnable problems -or- A model for premature saturation in backpropagation learning , 1996, ESANN.

[7]  Andreas Hadjiprocopis,et al.  Feed Forward Neural Network Entities , 1997, IWANN.

[8]  Zheng Tang,et al.  A modified error function for the backpropagation algorithm , 2004, Neurocomputing.

[9]  Jay S. Patel,et al.  Factors influencing learning by backpropagation , 1988, IEEE 1988 International Conference on Neural Networks.

[10]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[11]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1992, Math. Control. Signals Syst..

[12]  Tülay Adali,et al.  Approximation by Fully Complex Multilayer Perceptrons , 2003, Neural Computation.

[13]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1989, Math. Control. Signals Syst..

[14]  Chuan Wang,et al.  Training neural networks with additive noise in the desired signal , 1999, IEEE Trans. Neural Networks.

[15]  Tülay Adali,et al.  Fully Complex Multi-Layer Perceptron Network for Nonlinear Signal Processing , 2002, J. VLSI Signal Process..