●Chapter 1 Introduction
1.1 Feature Extraction
1.1.1 PCA and Subspace Tracking
1.1.2 PCA Neural Networks
1.1.3 Extension or Generalization of PCA
1.2 Basis for Subspace Tracking
1.2.1 Concept of Subspace
1.2.2 Subspace Tracking Method
1.3 Main Features of This Book
1.4 Organization of This Book
References
Chapter 2 Matrix Analysis Basics
2.1 Introduction
2.2 Singular Value Decomposition
2.2.1 Theorem and Uniqueness of SVD
2.2.2 Properties of SVD
2.3 Eigenvalue Decomposition
2.3.1 Eigenvalue Problem and Eigen Equation
2.3.2 Eigenvalue and Eigenvector
2.3.3 Eigenvalue Decomposition of Hermitian Matrix
2.3.4 Generalized Eigenvalue Decomposition
2.4 Rayleigh Quotient and Its Characteristics
2.4.1 Rayleigh Quotient
2.4.2 Gradient and Conjugate Gradient Algorithm for RQ
2.4.3 Generalized Rayleigh Quotient
2.5 Matrix Analysis
2.5.1 Differential and Integral of Matrix with Respect to Scalar
2.5.2 Gradient of Real Function with Respect to Real Vector
2.5.3 Gradient Matrix of Real Function
2.5.4 Gradient Matrix of Trace Function
2.5.5 Gradient Matrix of Determinant
2.5.6 Hessian Matrix
2.6 Summary
References
Chapter 3 Neural Networks for Principal Component Analysis
3.1 Introduction
3.2 Review of Neural Based PCA algorithms
3.3 Neural based PCA Algorithms Foundation
3.3.1 Hebbian Learning Rule
3.3.2 Oja's Learning Rule
3.4 Hebbian/Anti-Hebbian Rule based Principal Component Analysis
3.4.1 Subspace Learning Algorithms
3.4.2 Generalized Hebbian Algorithm
3.4.3 Learning Machine for Adaptive Feature Extraction via PCA
3.4.4 The Dot-Product-Decorrelation Algorithm
3.4.5 Anti-Hebbian Rule based Principal Component Analysis
3.5 Least Mean Squared Error based Principal Component Analysis
3.5.1 Least Mean Square Error Reconstruction Algorithm
3.5.2 Projection Approximation Subspace Tracking Algorithm
3.5.3 Robust RLS Algorithm
3.6 Optimization based Principal Component Analysis
3.6.1 Novel Information Criterion Algorithm
3.6.2 Coupled Principal Component Analysis
3.7 Nonlinear Principal Component Analysis
3.7.1 Kernel Principal Component Analysis
3.7.2 Robust/Nonlinear Principal Component Analysis
3.7.3 Autoassociative Network based Nonlinear PCA
3.8 Other PCA or Extensions of PCA
3.9 Summary
References
Chapter 4 Neural Networks for Minor Component Analysis
4.1 Introduction
4.2 Review of Neural Network Based MCA Algorithms
4.2.1 Extracting the First Minor Component
4.2.2 Oja's Minor Subspace Analysis
4.2.3 Self-stabilizing MCA
4.2.4 Orthogonal Oja Algorithm
4.2.5 Other MCA Algorithm
4.3 MCA EXIN Linear Neuron
4.3.1 The Sudden Divergence
4.3.2 The Instability Divergence
4.3.3 The Numerical Divergence
4.4 A Novel Self-stabilizing MCA Linear Neurons
4.4.1 A Self-stabilizing Algorithm for Tracking one MC
4.4.2 MS Tracking Algorithm
4.4.3 Computer Simulations
4.5 Total Least Squares Problem Application
4.5.1 A Novel Neural Algorithm for Total Least Squares Filtering
4.5.2 Computer Simulations
4.6 Summary
References
Chapter 5 Dual Purpose for Principal and Minor Component Analysis
5.1 Introduction
5.2 Review of Neural Network Based Dual Purpose Methods
5.2.1 Chen's Unified Stabilization Approach
5.2.2 Hasan's Self-normalizing Dual Systems
5.2.3 Peng's Unified Learning Algorithm to Extract Principal and Minor Components
5.2.4 Manton's Dual Purpose Principal and Minor Component Flow
5.3 A Novel Dual Purpose Method for Principal and Minor Subspace Tracking
5.3.1 Preliminaries
5.3.2 A Novel Information Criterion and Its Landscape
5.3.3 Dual Purpose Subspace Gradient Flow
5.3.4 Global Convergence Analysis
5.3.5 Numerical Simulations
5.4 Another Novel Dual Purpose Algorithm for Principal and Minor Subspace Analysis
5.4.1 The Criterion for PSA and MSA and Its Landscape
5.4.2 Dual Purpose Algorithm for PSA and MSA
5.4.3 Experimental Results
5.5 Summary
References
Chapter 6 Deterministic Discrete Time System for the Analysis of Iterative Algorithms
6.1 Introduction
6.2 Review of Performance Analysis Methods for Neural Network Based PCA Algorithms
6.2.1 Deterministic Continuous-Time System Method
6.2.2 Stochastic Discrete-Time System Method
6.2.3 Lyapunov Function Approach
6.2.4 Deterministic Discrete-Time System Method
6.3 DDT System of a Novel MCA Algorithm
6.3.1 Self-stabilizing MCA Extraction Algorithms
6.3.2 Convergence Analysis via DDT System
6.3.3 Computer Simulations
6.4 DDT System of a Unified PCA and MCA Algorithm
6.4.1 Introduction
6.4.2 A Unified Self-stabilizing Algorithm for PCA and MCA
6.4.3 Convergence Analysis
6.4.4 Computer Simulations
6.5 Summary
References
Chapter 7 Generalized Principal Component Analysis
7.1 Introduction
7.2 Review of Generalized Feature Extraction Algorithm
7.2.1 Mathew's Quasi-Newton Algorithm for Generalized Symmetric Eigenvalue Problem
7.2.2 Self-organizing Algorithms for Generalized Eigen Decomposition
7.2.3 Fast RLS-Like Algorithm for Generalized Eigen Decomposition
7.2.4 Generalized Eigenvector Extraction Algorithm Based on RLS Method
7.2.5 Fast Adaptive Algorithm for the Generalized Symmetric Eigenvalue Problem
7.2.6 Fast Generalized Eigenvector Tracking Based on the Power Method
7.2.7 Generalized Eigenvector Extraction Algorithm Based on Newton Method
7.2.8 Online Algorithms for Extracting Minor Generalized Eigenvector
7.3 A Novel Principal Generalized Eigenvector Extraction Algorithm
7.3.1 Algorithm Description
7.3.2 Convergence Analysis
7.3.3 Computer Simulations
7.4 Novel Multiple GMC Extraction Algorithm
7.4.1 A Weighted Information Criterion
7.4.2 Multiple GMCs Extraction Algorithm
7.4.3 Simulations and Application Experiments
7.5 Summary
References
Chapter 8 Coupled Principal Component Analysis
8.1 Introduction
8.2 Review of Coupled Principal Component Analysis
8.2.1 Moller's Coupled PCA Algorithm
8.2.2 Nguyen's Coupled Generalized Eigen-pairs Extraction Algorithm
8.2.3 Coupled Singular Value Decomposition of a Cross-covariance Matrix
8.3 Unified and Coupled Algorithm for Minor and Principal Eigen-pair Extraction
8.3.1 Coupled Dynamical System
8.3.2 The Unified and Coupled Learning Algorithms
8.3.3 Analysis of Convergence and Self-stabilizing Property
8.3.4 Simulation Experiments
8.4 Adaptive Coupled Generalized Eigen-pairs Extraction Algorithms
8.4.1 A Coupled Generalized System for GMCA and GPCA
8.4.2 Adaptive Implementation of Coupled Generalized Systems
8.4.3 Convergence Analysis
8.4.4 Numerical Examples
8.5 Summary
References
Chapter 9 Singular Feature Extraction and Its Neural Network
9.1 Introduction
9.2 Review of Cross-correlation Feature Method
9.2.1 Cross-correlation Neural Networks Model and Deflation Method
9.2.2 Parallel SVD Learning Algorithms on Double Stiefel Manifold
9.2.3 Double Generalized Hebbian Algorithm (DGHA) for SVD
9.2.4 Cross-associative Neural Network for SVD(CANN)
9.2.5 Coupled SVD of a Cross-Covariance Matrix
9.3 An Effective Neural Learning Algorithm for Extracting Cross- Correlation Feature
9.3.1 Preliminaries
9.3.2 Novel Information Criterion Formulation for PSS
9.3.3 Adaptive Learning Algorithm and Performance Analysis
9.3.4 Computer Simulations
9.4 Coupled Cross-correlation Neural Network Algorithm for Principal Singular Triplet Extraction of a Cross-Covariance Matrix
9.4.1 A Novel Information Criterion and A Coupled System
9.4.2 Online Implementation and Stability Analysis
9.4.3 Simulation Experiments
9.5 Summary
References
內容簡介
本書主要研究了一類非線性繫統的時域辨識、頻域辨識、總體很小二乘辨識及應用、非線性繫統建模、非線性繫統故障診斷應用等內容。本書內容大體上可分為三部分，部分研究了一類非線性繫統--Volterra級數模型基本理論，介紹了其時域分析和頻域分析方法；第二部分研究了Volterra級數模型的辨識與建模方法，介紹了Volterra級數模型的時域辨識和頻域辨識等多種迭代方法；第三部分研究了Volterra級數時域、頻域方法及混沌方法等在電路等復雜繫統參數估計、故障診斷中的應用。本書的很大一部分內容十分新穎，反映了靠前外非線性繫統建模與辨識領域方向上研究和應用的近期新進展。
