Composite Function Wavelet Neural Networks with Differential Evolution and Extreme Learning Machine

In this paper, we introduce a new learning method for composite function wavelet neural networks (CFWNN) by combining the differential evolution (DE) algorithm with extreme learning machine (ELM), in short, as CWN-E-ELM. The recently proposed CFWNN trained with ELM (CFWNN-ELM) has several promising features. But the CFWNN-ELM may have some redundant nodes due to the number of hidden nodes assigned a priori and the input weight matrix and the hidden node parameter vector randomly generated once and never changed during the learning phase. The introduction of DE into CFWNN-ELM is to search for the optimal network parameters and to reduce the number of hidden nodes used in the network. Simulations on several artificial function approximations, real-world data regressions and a chaotic signal prediction problem show some advantages of the proposed CWN-E-ELM. Compared with CFWNN-ELM, CWN-E-ELM has a much more compact network size and Compared with several relevant methods, CWN-E-ELM is able to achieve a better generalization performance.

[1]  Qinghua Zhang,et al.  Using wavelet network in nonparametric estimation , 1997, IEEE Trans. Neural Networks.

[2]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[3]  Hong Pan,et al.  Efficient Object Recognition Using Boundary Representation and Wavelet Neural Network , 2008, IEEE Transactions on Neural Networks.

[4]  Jianxin Xu,et al.  Nonlinear adaptive wavelet control using constructive wavelet networks , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[5]  Qinghua Zhang,et al.  Wavelet networks , 1992, IEEE Trans. Neural Networks.

[6]  A. Kai Qin,et al.  Evolutionary extreme learning machine , 2005, Pattern Recognit..

[7]  Kenneth Levenberg.  A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES , 1944 .

[8]  Bidyadhar Subudhi,et al.  Differential Evolution and Levenberg Marquardt Trained Neural Network Scheme for Nonlinear System Identification , 2008, Neural Processing Letters.

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

[10]  Mustafa Yilmaz,et al.  Classification of EMG signals using wavelet neural network , 2006, Journal of Neuroscience Methods.

[11]  Harold H. Szu,et al.  Neural network adaptive wavelets for signal representation and classification , 1992 .

[12]  Yongsheng Zhang,et al.  Wavelet Neural Networks for Nonlinear Time Series Analysis , 2004, ISNN.

[13]  Jun Zhang,et al.  Wavelet neural networks for function learning , 1995, IEEE Trans. Signal Process..

[14]  Chih-Jen Lin,et al.  A comparison of methods for multiclass support vector machines , 2002, IEEE Trans. Neural Networks.

[15]  Peter L. Bartlett,et al.  The Sample Complexity of Pattern Classification with Neural Networks: The Size of the Weights is More Important than the Size of the Network , 1998, IEEE Trans. Inf. Theory.

[16]  Zhiping Lin,et al.  Composite function wavelet neural networks with extreme learning machine , 2010, Neurocomputing.

[17]  Brian A. Telfer,et al.  Wavelet transforms and neural networks for compression and recognition , 1996, Neural Networks.

[18]  Chee Kheong Siew,et al.  Extreme learning machine: Theory and applications , 2006, Neurocomputing.

[19]  Feng Quanke,et al.  Fault Diagnosis Using Wavelet Neural Networks , 2003 .

[20]  D. Serre.  Matrices: Theory and Applications , 2002 .

[21]  Cheng-Jian Lin.  Wavelet Neural Networks with a Hybrid Learning Approach , 2006, J. Inf. Sci. Eng..

[22]  Gérard Dreyfus,et al.  Initialization by selection for wavelet network training , 2000, Neurocomputing.

[23]  Chee Kheong Siew,et al.  Can threshold networks be trained directly? , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[24]  Jin Bae Park,et al.  Adaptive Output Feedback Control of Flexible-Joint Robots Using Neural Networks: Dynamic Surface Design Approach , 2008, IEEE Transactions on Neural Networks.

[25]  Derong Liu,et al.  Wavelet Basis Function Neural Networks for Sequential Learning , 2008, IEEE Transactions on Neural Networks.