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Student Number 91541001 Author Sheng-Sung Yang(·¨²±ªQ) Author's Email Address yangss@chvs.hcc.edu.tw Statistics This thesis had been viewed 1780 times. Download 218 times. Department Electrical Engineering Year 2007 Semester 1 Degree Ph.D. Type of Document Doctoral Dissertation Language English Title Sensitivity Analysis of the Multilayer Perceptron due to the Errors of the Inputs and Weights & Improvements in BP and ES Algorithms Date of Defense 2007-11-28 Page Count 128 Keyword back-propagation evolutionary strategy multilayer perceptron sensitivity Abstract Multilayer Perceptron (MLP) is often used in some algorithms such as Back-Propagation (BP) algorithm, Evolutionary algorithm (EA), Extreme Learning Machine (ELM) algorithm, etc. Among these algorithms, BP and EA algorithms are more commonly operated in MLP structures to implement some applications than ELM is. Furthermore, the used MLP structures always affect the performances of these algorithms. Therefore, it is a substantial work to decide a feasible MLP structure (i.e., to decide number of layers and number of neurons in each layer) for each one of these algorithms. The main work of this dissertation is to analyze the adjustment of the output of the MLP due to the adjustments of the inputs and the weights between the neurons in adjacent layers (i.e., to analyze the sensitivity of the MLP due to the errors of the inputs and weights). Different MLP structure will lead to different sensitivity value. Based on the sensitivity values, it is feasible to choose a proper MLP structure for the related algorithm. In order to study the sensitivity of a MLP, we use the Central Limit Theorem (CLT) in the statistical computation of the sensitivity. Moreover, the CLT can also be extended to the sensitivity computation of the split-complex MLP (Split-CMLP); the Split-CMLP can be used in a complex signal system such as QPSK signal system, etc. Therefore, we analyze the sensitivity of both MLP and Split-CMLP in this dissertation. On the other hand, we combine the hierarchical structure and BP algorithm in this dissertation to improve the performance of the standard BP algorithm, and this new algorithm is named as HBP algorithm. Additionally, we also introduce an approach in this dissertation to decide the operation parameters of the Evolutionary Strategy (ES) algorithm-the most popular one of the Evolutionary algorithms, to improve its performance. Table of Content Chapter 1 Introduction1

1.1 Motivation of the Dissertation1

1.2 Overview of the Dissertation4

1.3 Organization of the Dissertation6

Chapter 2 Sensitivity of the Multilayer Perceptron due to the Errors of the Inputs and Weights8

2.1 MLP Model8

2.2 Sensitivity Computation of the MLP11

2.3 Sensitivity Analysis of the MLP22

2.4 Summary31

Chapter 3 Sensitivity of the Split-Complex valued Multilayer Perceptron due to the Errors of the Inputs and Weights33

3.1 Split-CMLP Model33

3.2 Sensitivity Computation of the Split-CMLP37

3.3 Analysis of the Sensitivity for the Split-CMLP49

3.4 Summary59

Chapter 4 Hierarchical Back-Propagation Algorithm for an MLP Decision Feedback Equalizer61

4.1 MLP-Based DFE61

4.2 Hierarchical BP (HBP) Algorithm65

4.3 Computer Simulations72

4.4 Summary80

Chapter 5 Improving the Evolutionary Strategy (ES) Algorithm by Choosing Appropriate Parameters81

5.1 Evolutionary Strategy (ES)81

5.2 Analysis of Mutation Rates83

5.3 Simulation Results85

5.4 Summary93

Chapter 6 Conclusions95

References98

Appendix A104

Appendix B109

Appendix C Author¡¦s Information113

Appendix D Publication List114Reference [1] M. Stevenson, R. Winter, and B. Widrow, ¡§Sensitivity of feedforward neural networks to weight errors,¡¨ IEEE Trans. Neural Networks, vol. 1, pp. 71-80, Mar. 1990.

[2] A. Y. Cheng and D. S. Yeung, ¡§Sensitivity analysis of neocognitron,¡¨ IEEE Trans. Syst., Man, Cybern. C, vol. 29, pp. 238-249, May. 1999.

[3] S. W. Piche, ¡§The selection of weight accuracies for Madalines,¡¨ IEEE Trans. Neural Networks, vol. 6, pp. 432-445, Mar. 1995.

[4]S. Hashem, ¡§Sensitivity analysis for feedforward artificial neural networks with differentiable activation functions,¡¨ in Proc. IJCNN¡¦92, vol. 1, Baltimore, MD, 1992, pp. 419-424.

[5]L. Fu and T. Chen, ¡§Sensitivity analysis for input vector in multilayer feedforward neural networks,¡¨ in Proc. IEEE Int. Conf. Neural Networks, vol. 1, San Francisco, CA, 1993, pp. 215-218.

[6]J. M. Zurada, A. Malinowski, and S. Usui, ¡§Perturbation method for deleting reduntant inputs of perceptron networks,¡¨ Neurocomput., vol. 14, pp. 177-193, 1997.

[7]A. P. Engelbrecht and I. Cloete, ¡§A sensitivity analysis algorithm for pruning feedforward neural networks,¡¨ in Proc. IEEE Int. Conf. Neural Networks, vol. 2, Washington, DC, 1996, pp. 1274-1277.

[8]A. P. Engelbrecht, L. Fletcher, and I. Cloete, ¡§Variance analysis of sensitivity information for pruning feedforward neural networks,¡¨ in Proc. IEEE Int. Conf. Neural Networks, Washington, DC, 1999, pp.1829-1833.

[9]J. Y. Choi and C.-H. Choi, ¡§Sensitivity analysis of multilayer perceptron with differentiable activation functions,¡¨ IEEE Trans. Neural Networks, vol. 3, pp. 101-107, Jan. 1992.

[10]S.-H. Oh and Y. Lee, ¡§Sensitivity analysis of a single hidden-layer neural networks with threshold function,¡¨ IEEE Trans. Neural Networks, vol. 6, pp. 1005-1007, July 1995.

[11]Xiaoqin Zeng and Daniel S. Yeung, ¡§Sensitivity analysis of multilayer perceptron to input and weight perturbations,¡¨ IEEE Trans. Neural Networks, vol. 12, pp. 1358-1366, Nov. 2001.

[12]Xiaoqin Zeng, Yingfeng Wang, and Kang Zhang, ¡§Computation of Adalines¡¦ Sensitivity to Weight Perturbation,¡¨ IEEE Trans. Neural Networks, vol. 17, pp. 515-519, Mar. 2006.

[13] Sheng-Sung Yang, Chia-Lu Ho and Sammy Siu, ¡§Sensitivity analysis of the Split-Complex valued multilayer perceptron due to the errors of the i.i.d. inputs and weights,¡¨ IEEE Trans. Neural Networks, vol. 18, pp. 1280-1293, September 2007.

[14]S.Siu, G.Gibson, and C.Cowan, ¡§Decision feedback equalization using neural network structures and performance comparison with standard architectures,¡¨ IEE proceedings, Vol. 137, part.1, No. 4, pp. 221-225, 1990.

[15]S.Siu, and C.F.N.Cowan, ¡§Performance analysis of the norm back propagation algorithm for adaptive equalization,¡¨ IEE Proceedings-F, Vol. 140, No.1, February, pp.43- 47, 1993.

[16]S.Siu, C.H.Chang, and C.H.Wei, ¡§ Norm Back Propagation Algorithm for Adaptive Equalization,¡¨ IEEE Trans. on Circuits and Systems II, Vol. 42, No. 9, pp. 604-607, September 1995.

[17]G.J.Gibson, S. Siu, and C.F.N. Cowan, ¡§The application of nonlinear structures to the reconstruction of binary signals,¡¨ IEEE Trans. Signal Processing, Vol. 39, No.8, pp. 1877-1884, 1991.

[18]R.P.Lippmann, ¡§An introduction to computing with neural nets,¡¨ IEEE ASSP Magazine, Vol. 4, No. 2, pp. 4-22, 1987.

[19]G.-B. Huang, Q.-Y. Zhu, and C.-K. Siew, ¡§Extreme learning machine,¡¨ in Technical Report ICIS/03/2004, (School of Electrical and Electronic Engineering, Nayang Technological University, Singapore), Jan. 2004.

[20]T.-K. Woo, ¡§ Fast hierarchical least mean square algorithm,¡¨ IEEE Signal Processing Lett., Vol.8, pp. 289-291, Nov. 2001.

[21]T.-K. Woo, ¡§ HRLS: A more efficient RLS algorithm for adaptive FIR filtering,¡¨ IEEE Commun. Lett., Vol. 5, pp. 81-84, Mar. 2001.

[22]V. H. Nascimento, ¡§ Analysis of the hierarchical LMS algorithm,¡¨ IEEE Signal Processing Lett., Vol. 10, pp.78-81, Mar. 2003.

[23]S.-S. Yang, C.-L. Ho and C.-M. Lee, ¡§HBP: Improvement in BP Algorithm for an Adaptive MLP Decision Feedback Equalizer, ¡¨ IEEE Trans. on Circuits and Systems II, vol. 53, no.3, pp.240-244, Mar. 2006.

[24]P. Power, F. Sweeney, and C.F.N. Cowan, ¡§EA crossover schemes for a MLP channel equalizer,¡¨ Electronics, Circuits and Systems, 1999, Proceedings of ICECES¡¦99, The 6th IEEE International Conference, vol.1, pp.407-410, 1999.

[25]T. Back, Evolutionary algorithm in theory and practice: evolution strategies, evolution programming, genetic algorithms, Oxford, 1996.

[26]T.Back and H.-P.Schwefel, ¡§Evolutionary computation: An overview,¡¨ in Proc. IEEE Int. Conf. Evolutionary Computation, pp.20-29, 1996.

[27]Hans-Georg Beyer, The Theory of Evolution Strategies, Spring, 2001.

[28]Hussein A. Abass, ¡§Speeding Up Back-propagation Using Multi-objective Evolutionary Algorithms,¡¨ Neural Computation, vol.15, no.11, pp.2704-2726, November, 2003.

[29]S.C.Chan, W.Liu, and K.L.Ho, ¡§Multiplierless Perfect Reconstruction Modulated Filter Banks with Sum-of-Powers-of-Two Coefficients,¡¨ IEEE Signal Processing Letters, vol.8, no.6, pp.163-166, 2001.

[30]R.Thamvichai, Tamal Bose, and Randy L. Haupt, ¡§Design of 2-D Multiplierless IIR Filters Using the Genetic Algorithm,¡¨ IEEE Trans. on Circuits and Systems I, vol.49, no.6, pp.878-882, 2002.

[31]Y.-H. Lee, M. Kawamata, and T. Higuchi, ¡§GA-based design of multiplierless 2-D state-space digital filters with low roundoff noise,¡¨ Proc. IEEE., vol.145, pp.118-124, 1998.

[32]V. Schnecke and O. Vornberger, ¡§Genetic design of VLSI-Layouts,¡¨ in Proc. Int. Conf. Genetic Algorithms in Engineering Systems: Innovations and Applications, pp.430-435, 1995.

[33]S.Siu, Chia-Lu Ho, and C.M.Lee, ¡§TSK Based Decision Feedback Equalizer using Evolutionary Algorithms Applied to QAM Communication Systems¡¨, IEEE Trans. on Circuits and Systems II, vol. 52, no.9, pp.596-600, Sept. 2005.

[34]Athanasios Papoulis, Probability, random variables, and stochastic processes, 3rd Edition, McGraw-Hill, Inc. 1991.

[35] Kim T. and Adali T., ¡§ Fully Complex Backpropagation for Constant Envelop Signal Processing, ¡¨ Proc. of IEEE Workshop on Neural Networks for Sig. Proc., pp. 231-240, Sydney, Dec. 2000.

[36]Kim T. and Adali T., ¡§ Nonlinear Satellite Channel Equalization Using Fully Complex Feed-Forward Neural Networks, ¡¨ Proc. of IEEE Workshop on Nonlinear Signal and Image Processing, pp. 141-150, Baltimore, June, 2001.

[37]H. Leung and S. Haykin, ¡§The complex backpropagation algorithm,¡¨ IEEE Trans. Signal Processing, vol. 39, pp. 2101-2104, 1991.

[38]N. Benvenuto and F. Piazza, ¡§On the complex backpropagation algorithm,¡¨ IEEE Trans. Signal Processing, vol. 40, pp. 967-969, 1992.

[39]C. H. Chang, S. Siu and C. H. Wei, ¡§Decision feedback equalization using complex backpropagation algorithm,¡¨ in Proc. of IEEE International Symposium on Circuits and Systems, Hong Kong, pp. 589-592, June 1997.

[40]S. Tamura and M. Tateishi, ¡§Capabilities of a four-layered feedforward neural network: Four layers versus three,¡¨ IEEE Transactions on Neural Networks, vol. 8, no. 2, pp. 251-255, 1997.

[41]S. Siu, S.-S. Yang, C.-M. Lee, and C.-L. Ho, ¡§Improving the Back-Propagation Algorithm Using Evolutionary Strategy,¡¨ IEEE Trans. on Circuits and Systems II, vol. 54, no.2, pp.171-175, Feb. 2007.

[42]H.-G. Byer and K. Deb, ¡§On Self-Adaptive Features in Real-Parameter Evolutionary Algorithms,¡¨ IEEE Trans. on Evolutionary Computation, vol.5, no.3, pp.250-270, 2001.Advisor Chia-Lu Ho(¶P¹Å«ß)

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