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Efficient Online Learning Algorithms for Total Least Square Problems（总体最小二乘问题的有效在线学习算法）


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Efficient Online Learning Algorithms for Total Least Square Problems（总体最小二乘问题的有效在线学习算法）
  • 书号：9787030848703
    作者：孔祥玉,冯大政
  • 外文书名：
  • 装帧：圆脊精装
    开本：B5
  • 页数：269
    字数：
    语种：en
  • 出版社：科学出版社
    出版时间：2026-01-01
  • 所属分类：
  • 定价： ￥258.00元
    售价： ￥193.50元
  • 图书介质:
    纸质书

  • 购买数量： 件  可供
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本书主要介绍作者近20年来的科研成果，包括递归TLS算法、近似逆幂迭代TLS算法、基于神经网络的MCA算法、基于神经网络的SVD算法、基于神经网络的TLS算法、非高斯噪声下的TLS算法、TLS算法的性能分析方法等。为了使读者更快地理解和掌握本书所提供的新方法，在介绍每一章的新方法之前，提供了一个专门的章节来回顾密切相关的几个基本模型。全书提供了大量新方法的详细步骤，提出的所有新算法或方法都通过数值模拟或实际工程应用进行了测试和验证。
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目录

  • Contents
    1 Introduction 1
    1.1 An Overview of Total Least Square 1
    1.1.1 Total Least Square Problems 1
    1.1.2 Total Least Square Methods 3
    1.1.3 Related Monographs for Total Least Square 4
    1.2 Aim and Main Features of This Book 6
    1.2.1 Aim of This Book 6
    1.2.2 Main Features of This Book 6
    1.3 Organization of This Book 8
    References 9
    2 Total Least Square Problems 13
    2.1 Preliminaries 13
    2.1.1 Overdetermined Linear Equations and SVD of Matrix 13
    2.1.2 Ordinary Least Squares (OLS) Problems 16
    2.2 Classical TLS Problem 16
    2.2.1 Basic TLS Problems 17
    2.2.2 OLS and TLS Geometric Considerations 18
    2.2.3 Multidimensional TLS Problem 20
    2.2.4 Non-generic Unidimensional TLS Problem 23
    2.3 Extension of TLS Problem 25
    2.3.1 Mixed OLS-TLS Problem 25
    2.3.2 Statistical Properties and Validity 26
    2.3.3 Basic Data Least Squares Problem 27
    2.3.4 Generalized TLS Problem 28
    2.3.5 Weighted TLS Problem 31
    2.3.6 Constrained TLS Problem 32
    2.3.7 Structured TLS Problem 33
    2.3.8 TLS in Nonlinear EIV Models 34
    2.3.9 TLS Under Non-gaussian Noises 35
    2.4 Summary 36
    References 36
    3 Total Least Square Methods 39
    3.1 TLS Solution 39
    3.2 Partial TLS Algorithm 42
    3.3 Iterative Computation Methods 42
    3.3.1 Direct Versus Iterative Computation Methods 43
    3.3.2 Inverse Iteration 43
    3.3.3 Chebyshev Iteration 44
    3.3.4 Lanczos Methods 44
    3.3.5 Rayleigh Quotient Iteration 45
    3.4 Rayleigh Quotient Minimization Non-neural Methods 45
    3.4.1 Davila's Recursive TLS Algorithm 46
    3.4.2 Feng's Fast Recursive TLS Algorithm 46
    3.4.3 Feng's Fast Approximate Inverse Power Iterative TLS Algorithm 47
    3.5 Neural Networks Methods for TLS 47
    3.5.1 Neural Networks Methods for MCA 47
    3.5.2 Neural Networks Methods for SVD 49
    3.5.3 Neural Networks that Iterate Only in the TLS Hyperplane 50
    3.6 Other Methods of Extended TLS Problems 52
    3.6.1 Weighted TLS Algorithms 52
    3.6.2 Constrained TLS Algorithm 53
    3.6.3 Structured TLS Solution 53
    3.6.4 TLS in Nonlinear EIV Models 54
    3.6.5 TLS Under Non-Gaussian Noises 54
    3.7 Conclusions 55
    References 55
    4 Fast Recursive TLS Algorithms 59
    4.1 Introduction 59
    4.2 Review of Davila's RTLS Algorithm for FIR Adaptive Filtering 61
    4.2.1 RLS Filter Bias and Mean Squared Error for IR Estimation 61
    4.2.2 TLS for Adaptive FIR Filters 63
    4.2.3 Recursive TLS Algorithm 64
    4.3 A Fast Recursive TLS Algorithm for Adaptive FIR Filtering 66
    4.3.1 TLS Problems in Signal Processing 67
    4.3.2 Landscape of Criterion 69
    4.3.3 New RTLS Algorithm 70
    4.3.4 Convergence Analysis 72
    4.3.5 Simulations and Conclusions 73
    4.4 A Fast Recursive TLS Algorithm for Adaptive IIR Filtering 75
    4.4.1 TLS Problems in Adaptive IIR Filtering and N-RTLS Algorithm 75
    4.4.2 Algorithm Convergence 80
    4.4.3 Simulations and Conclusions 82
    4.5 Summary 85
    References 86
    5 Approximate Inverse Power Iteration TLS Algorithm 89
    5.1 Introduction 89
    5.2 Review of Inverse Power Iteration 90
    5.3 AIP Iteration Algorithm for Adaptive TLS FIR Filtering 92
    5.3.1 Preliminaries 92
    5.3.2 AIP Iteration Algorithm 95
    5.3.3 Algorithm Convergence 99
    5.3.4 Simulations Examples and Conclusion 102
    5.4 An AIP Algorithm for Adaptive Extraction of Minor Subspace 104
    5.4.1 Proposed Adaptive Tracking Algorithm of MS 104
    5.4.2 Theoretical Analysis of Algorithm 107
    5.5 Summary 112
    References 113
    6 Neural-Based MCA Algorithms for Adaptive TLS 115
    6.1 Introduction 115
    6.2 Review of Neural-Network-Based MCA Algorithms 117
    6.2.1 Oja's MCA Algorithms 117
    6.2.2 Self-stabilizing MCA Algorithms 118
    6.2.3 Orthogonal Oja's Algorithms 118
    6.2.4 Coupled MCA Algorithms 118
    6.3 Novel Parallel Multiple MCs Extraction Algorithm by Diagonal Matrix 119
    6.3.1 Preliminary and Novel Algorithm 119
    6.3.2 Fixed Points Analysis 121
    6.3.3 Stability on the Manifold 124
    6.3.4 Simulation Experiments and Conclusion 126
    6.4 A Weighted Information Criterion and Multiple MC Algorithm 128
    6.4.1 Preliminaries 128
    6.4.2 A Weighted Information Criterion and Its Landscape 129
    6.4.3 Adaptive Multiple MCs Extraction Algorithms 134
    6.4.4 Convergence Analysis 137
    6.4.5 Simulations Experiments and Conclusions 139
    6.5 A Coupled Minor Component Analysis Algorithm 147
    6.5.1 Coupled Dynamical System 147
    6.5.2 Coupled MCA Learning Algorithms 149
    6.5.3 Analysis of Convergence and Self-stabilizing Property 151
    6.5.4 Simulation and Conclusions 153
    6.6 Summary 158
    References 158
    7 Neural-Based SVD Algorithms for Adaptive TLS 161
    7.1 Introduction 161
    7.2 Review of Neural-Based SVD Algorithms 163
    7.2.1 Parallel Learning Algorithms on Double Stiefel Manifold 163
    7.2.2 Cross-Associative Neural Network for SVD (CANN) 165
    7.2.3 Coupled SVD of a Cross-Covariance Matrix 167
    7.3 A Neural Network for SVD of Non-squared Data Matrix 169
    7.3.1 A Novel Recurrent Neural Network 169
    7.3.2 Stability Analysis of Algorithm 172
    7.3.3 Simulation Experiments and Conclusions 174
    7.4 A Fast and Effective Neural Network Algorithm to Perform SVD 176
    7.4.1 Preliminary 177
    7.4.2 Novel Information Criterion and Algorithm 178
    7.4.3 Convergence Analysis 180
    7.4.4 Experiments and Conclusions 184
    7.5 Coupled Neural Network Algorithm for PST Extraction 192
    7.5.1 Novel Information Criterion and Its Coupled System 193
    7.5.2 Experiments and Conclusions 196
    7.6 Summary 198
    References 199
    8 Neural-Based TLS Algorithms 201
    8.1 Introduction 201
    8.2 Review of Neural-Based TLS Algorithms 202
    8.2.1 The Hopfield-Like Neural Network of Luo, Li, and He 202
    8.2.2 The Linear Neuron of Gao, Ahmad, and Swamy 203
    8.2.3 The Linear Neurons of Cichocki and Unbehauen 205
    8.2.4 The TLS EXIN Neural Network and Its Modified Version 206
    8.2.5 The LS-TLS Neural Algorithm of Bruce and Williamson 206
    8.3 A Self-stabilizing Neural Algorithm for TLS Filtering 209
    8.3.1 The TLS Linear Neuron with a Self-stabilizing Algorithm 209
    8.3.2 Self-stabilizing and Stability 211
    8.3.3 Simulation of Algorithm 216
    8.4 Conclusion 221
    References 221
    9 TLS Algorithm Under Non-Gaussian Noises 223
    9.1 Introduction 223
    9.2 Review of the LS/TLS Method Under Non-Gaussian Noises 224
    9.2.1 The LS Method Under Non-Gaussian Noise 224
    9.2.2 TLS Algorithm with Input and Output of the Same Noise Intensity 228
    9.3 Mixed LS-TLS Algorithm Under Non-Gaussian Noises 232
    9.3.1 Partial Input and Output Contaminated with Non-Gaussian Noises 232
    9.3.2 Disparate Input and Output Non-Gaussian Noises 235
    9.3.3 Input Non-Gaussian Noises Only 238
    9.4 Simulation Experiments and Analysis 241
    9.4.1 Experiment of NG-TLS Algorithm 241
    9.4.2 Experiment of NG-LS-TLS Algorithm 243
    9.5 Summary 246
    References 246
    10 Performance Analysis Methods of TLS Algorithms 247
    10.1 Introduction 247
    10.2 Review of the Analysis Methods of MCA/TLS Algorithms 248
    10.2.1 Deterministic Continuous-Time System Method 248
    10.2.2 Stochastic Discrete-Time System Method 249
    10.2.3 Lyapunov Function Approach 250
    10.2.4 Fixed Pointed Method 251
    10.2.5 Deterministic Discrete-Time System Method 252
    10.3 Convergence of Novel Generalized MCA Algorithm via DDT 252
    10.3.1 Algorithm Presentation 252
    10.3.2 Self-stabilizing Analysis 254
    10.3.3 Dynamic Characteristic of the GChen Algorithm 255
    10.3.4 Numerical Simulations and Conclusions 263
    10.4 Summary 269
    References 269
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