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Principal Component Analysis Networks and Algorithms [electronic resource] / by Xiangyu Kong, Changhua Hu, Zhansheng Duan.

By: Kong, Xiangyu [author.].
Contributor(s): Hu, Changhua [author.] | Duan, Zhansheng [author.] | SpringerLink (Online service).
Material type: materialTypeLabelBookPublisher: Singapore : Springer Nature Singapore : Imprint: Springer, 2017Edition: 1st ed. 2017.Description: XXII, 323 p. 86 illus., 41 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9789811029158.Subject(s): Computational intelligence | Pattern recognition systems | Neural networks (Computer science)  | Statistics  | Algorithms | Signal processing | Computational Intelligence | Automated Pattern Recognition | Mathematical Models of Cognitive Processes and Neural Networks | Statistical Theory and Methods | Algorithms | Signal, Speech and Image ProcessingAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 006.3 Online resources: Click here to access online
Contents:
Introduction -- Eigenvalue and singular value decomposition -- Principal component analysis neural networks -- Minor component analysis neural networks -- Dual purpose methods for principal and minor component analysis -- Deterministic discrete time system for PCA or MCA methods -- Generalized feature extraction method -- Coupled principal component analysis -- Singular feature extraction neural networks.
In: Springer Nature eBookSummary: 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.
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Introduction -- Eigenvalue and singular value decomposition -- Principal component analysis neural networks -- Minor component analysis neural networks -- Dual purpose methods for principal and minor component analysis -- Deterministic discrete time system for PCA or MCA methods -- Generalized feature extraction method -- Coupled principal component analysis -- Singular feature extraction neural networks.

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.

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