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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 1811 times. Download 236 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

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