Subspace Learning of Neural Networks  book cover
1st Edition

Subspace Learning of Neural Networks

ISBN 9781138112681
Published June 14, 2017 by CRC Press
248 Pages 84 B/W Illustrations

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Book Description

Using real-life examples to illustrate the performance of learning algorithms and instructing readers how to apply them to practical applications, this work offers a comprehensive treatment of subspace learning algorithms for neural networks. The authors summarize a decade of high quality research offering a host of practical applications. They demonstrate ways to extend the use of algorithms to fields such as encryption communication, data mining, computer vision, and signal and image processing to name just a few. The brilliance of the work lies with how it coherently builds a theoretical understanding of the convergence behavior of subspace learning algorithms through a summary of chaotic behaviors.

Table of Contents


Chapter 1. Introduction

1.1 Introduction

1.1.1 Linear Neural Networks

1.1.2 Subspace Learning

1.2 Subspace Learning Algorithms

1.2.1 PCA Learning Algorithms

1.2.2 MCA Learning Algorithms

1.2.3 ICA Learning Algorithms

1.3 Methods for Convergence Analysis

1.3.1 SDT Method

1.3.2 DCT Method

1.3.3 DDT Method

1.4 Block Algorithms

1.5 Simulation Data Set and Notation

1.6 Conclusions

Chapter 2. PCA Learning Algorithms with Constants Learning Rates

2.1 Oja’s PCA Learning Algorithms

2.1.1 The Algorithms

2.1.2 Convergence Issue

2.2 Invariant Sets

2.2.1 Properties of Invariant Sets

2.2.2 Conditions for Invariant Sets

2.3 Convergence analysis via DDT Method

2.3.1 Problem Formulation

2.3.2 Proof of Convergence

2.4 Convergence analysis of Xu’s LMSER algorithm

2.5 Discussions

2.5.1 Learning Rates Selection

2.5.2 Initial Points Selection

2.6 Conclusions

Chapter 3. PCA Learning Algorithms with Adaptive Learning Rates

3.1 Introduction

3.2 Adaptive Learning Rates

3.3 Oja’s Algorithm with Adaptive Learning Rates

3.4 Convergence Analysis of Oja’s Algorithm with Adaptive Learning Rates

3.4.1 Boundedness

3.4.2 Global Convergence

3.5 Simulations and Discussions

3.6 Conclusions

Chapter 4. GHA PCA Learning Algorithms

4.1 GHA PCA Learning Alogrithms

4.1.1 The Algorithms

4.1.2 Convergence Issue

4.2 Problem Formulation

4.3 Convergence Analysis via DDT Method

4.3.1 Outline of Proof

4.3.2 Detail of Proof

4.4 Discussions and Simulations

4.4.1 Example 1

4.4.2 Example 2

4.4.3 Example 3

4.5 Conclusions

Chapter 5. MCA Learning Algorithms

5.1 MCA Learning Algorithms

5.1.1 The Algorithms

5.1.2 Convergence Issue

5.2 Invariant Sets

5.2.1 Properties of Invariant Sets

5.2.2 Conditions for Invariant Sets

5.3 Convergence Analysis via DDT Methods

5.3.1 Problem Formulation

5.3.2 Proof of Convergence

5.4 Simulations and Discussions

5.5 Conclusions

Chapter 6. ICA Learning Algorithms

6.1 Hyvarinen-Oja Algorithm

6.1.1 The Algorithm

6.1.2 Convergence Issue

6.2 Invariant Sets

6.2.1 Properties of Invariant Sets

6.2.2 Conditions for Invariant Sets

6.3 Convergence Analysis via DDT Method

6.3.1 Problem Formulation

6.3.2 Proof of Convergence

6.4 Simulations and Discussions

6.5 Conclusions

Chapter 7. Chaotic Behaviors Arising from Learning Algorithms

7.1 Introduction to Chaotic Behaviors

7.1.1 Chaotic Behaviors

7.1.2 Lyapunov Exponents

7.2 Chaotic Behaviors Arising from PCA Learning Algorithms

7.2.1 Computing of Lyapunov Exponents

7.2.2 Simulation Results

7.3 Chaotic Behaviors Arising from MCA Learning Algorithms

7.3.1 Computing of Lyapunov Exponents

7.3.2 Simulation Results

7.4 Chaotic Behaviors Arising from ICA Learning Algorithms

7.4.1 Computing of Lyapunov Exponents

7.4.2 Simulation Results

7.5 Conclusions

Chapter 8. Multi-Block-Based MCA for Nonlinear Surface Fitting

8.1 Introduction

8.2 MCA Neural Network for Nonlinear Surface Fitting

8.3 Multi-Block-Based MCA

8.4 Multi-Block-Based MCA for Nonlinear Surface Fitting

8.5 Conclusions

Chapter 9. A ICA Algorithm for Extracting Fetal Electrocardiogram

9.1 Introduction

9.2 Problem Formulation

9.3 The Proposed Algorithm

9.4 Extracting Fetal Electrocardiogram

9.5 Conclusions

Chapter 10. Some Applications of PCA Neural Networks

10.1 Introduction

10.2 Rigid Medical Image Registration

10.2.1 Introduction

10.2.2 Method

10.2.3 Simulation

10.2.4 Conclusions

10.3 A Chaotic Encryption System Based on PCA Algorithm

10.3.1 Chaos and Encryption

10.3.2 A Chaotic Encryption System

10.3.3 Simulation

10.3.4 Conclusion

10.4 Conclusion

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Jian Cheng LV and Zhang Yi are affiliated with the Machine Intelligence Lab of the College of Computer Science at Sichuan University. Jiliu Zhou is affiliated with the College of Computer Science at Sichuan University.