Kong X., Hu C., Duan Zh. Principal Component Analysis Networks & Algorithms

New York: Springer, 2017. — 333 p. — ISBN: 978-981-10-2913-4.This book not only provides a comprehensive introduction to neural-based PCA methods in control science, but also presents many novel PCA algorithms and their extensions and generalizations, e.g., dual purpose, coupled PCA, GED, neural based SVD algorithms, etc. It also discusses in detail various analysis methods for the convergence, stabilizing, self-stabilizing property of algorithms, and introduces the deterministic discrete-time systems method to analyze the convergence of PCA/MCA algorithms. Readers should be familiar with numerical analysis and the fundamentals of statistics, such as the basics of least squares and stochastic algorithms. Although it focuses on neural networks, the book only presents their learning law, which is simply an iterative algorithm. Therefore, no a priori knowledge of neural networks is required. This book will be of interest and serve as a reference source to researchers and students in applied mathematics, statistics, engineering, and other related fields.Feature Extraction
Basis for Subspace Tracking
Main Features of This Book
Organization of This BookMatrix Analysis BasicsSingular Value Decomposition
Eigenvalue Decomposition
Rayleigh Quotient and Its Characteristics
Matrix AnalysisNeural Networks for Principal Component AnalysisReview of Neural-Based PCA Algorithms
Neural-Based PCA Algorithms Foundation
Hebbian/Anti-Hebbian Rule-Based Principal Component Analysis
Least Mean Squared Error-Based Principal Component Analysis
Optimization-Based Principal Component Analysis
Nonlinear Principal Component Analysis
Other PCA or Extensions of PCANeural Networks for Minor Component AnalysisReview of Neural Network-Based MCA Algorithms
MCA EXIN Linear Neuron
A Novel Self-stabilizing MCA Linear Neurons
Total Least Squares Problem ApplicationDual Purpose for Principal and Minor Component AnalysisReview of Neural Network-Based Dual-Purpose Methods
A Novel Dual-Purpose Method for Principal and Minor Subspace Tracking
Another Novel Dual-Purpose Algorithm for Principal and Minor Subspace AnalysisDeterministic Discrete-Time System for the Analysis of Iterative AlgorithmsReview of Performance Analysis Methods for Neural NetworkBased PCA Algorithms
DDT System of a Novel MCA Algorithm
DDT System of a Unified PCA and MCA AlgorithmGeneralized Principal Component AnalysisReview of Generalized Feature Extraction Algorithm
A Novel Minor Generalized Eigenvector Extraction Algorithm
Novel Multiple GMC Extraction AlgorithmCoupled Principal Component AnalysisReview of Coupled Principal Component Analysis
Unified and Coupled Algorithm for Minor and Principal Eigen Pair Extraction
Adaptive Coupled Generalized Eigen Pairs Extraction AlgorithmsSingular Feature Extraction and Its Neural NetworksReview of Cross-Correlation Feature Method
An Effective Neural Learning Algorithm for Extracting Cross-Correlation Feature
Coupled Cross-Correlation Neural Network Algorithm for Principal Singular Triplet Extraction of a Cross-Covariance Matrix