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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.