Principal Component Analysis Networks and Algorithms
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 algorithm
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ncipal Component Analysis Networks and Algorithms
Principal Component Analysis Networks and Algorithms
Xiangyu Kong Changhua Hu Zhansheng Duan •
Principal Component Analysis Networks and Algorithms
123
Zhansheng Duan Center for Information Engineering Science Research Xi’an Jiaotong University Xi’an, Shaanxi China
Xiangyu Kong Department of Control Engineering Xi’an Institute of Hi-Tech Xi’an China Changhua Hu Department of Control Engineering Xi’an Institute of Hi-Tech Xi’an China
ISBN 978-981-10-2913-4 DOI 10.1007/978-981-10-2915-8
ISBN 978-981-10-2915-8
(eBook)
Jointly published with Science Press, Beijing, China Library of Congress Control Number: 2016955323 © Science Press, Beijing and Springer Nature Singapore Pte Ltd. 2017 This work is subject to copyright. All rights are reserved by the Publishers, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publishers, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publishers nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #22-06/08 Gateway East, Singapore 189721, Singapore
To all the researchers with original contributions to principal component analysis neural networks and algorithms —Xiangyu Kong, Changhua Hu and Zhansheng Duan
Preface
Aim of This book The aim of this book is to (1) to explore the relationship between principal component analysis (PCA), neural network, and learning algorithms and provide an introduction to adaptive PCA methods and (2) to present many novel PCA algorithms, their extension/generalizations, and their performance analysis. In data analysis, one very important linear technique to extract information from data is principal component analysis (PCA). Here, the principal components (PCs) are the directions in which the data have the largest variances and capture most of the information content of data. They correspond to the eigenvectors associated with the largest eigenvalues of the autocorrelation matrix of the data vectors. On the contrary, the eigenvectors that correspond to the small
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