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JSS Research Series in Statistics

Nonlinear Principal Component Analysis and Its Applications

Authors: Mori, Yuichi, Kuroda, Masahiro, Makino, Naomichi

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  • Shows that PCA, nonlinear PCA, and MCA can be integrated as a single formulation, which can easily be extended to several applications
  • Provides an acceleration algorithm that speeds up the convergent sequences generated by the alternating least squares and is a remedy for computational cost
  • Introduces applications related to nonlinear PCA: variable selection for mixed measurement levels data, sparse multiple correspondence analysis, and joint dimension reduction and clustering
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eBook 46,00 €
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  • ISBN 978-981-10-0159-8
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Softcover 57,19 €
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  • ISBN 978-981-10-0157-4
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About this book

This book expounds the principle and related applications of nonlinear principal component analysis (PCA), which is useful method to analyze mixed measurement levels data. In the part dealing with the principle, after a brief introduction of ordinary PCA, a PCA for categorical data (nominal and ordinal) is introduced as nonlinear PCA, in which an optimal scaling technique is used to quantify the categorical variables. The alternating least squares (ALS) is the main algorithm in the method. Multiple correspondence analysis (MCA), a special case of nonlinear PCA, is also introduced. All formulations in these methods are integrated in the same manner as matrix operations. Because any measurement levels data can be treated consistently as numerical data and ALS is a very powerful tool for estimations, the methods can be utilized in a variety of fields such as biometrics, econometrics, psychometrics, and sociology. In the applications part of the book, four applications are introduced: variable selection for mixed measurement levels data, sparse MCA, joint dimension reduction and clustering methods for categorical data, and acceleration of ALS computation. The variable selection methods in PCA that originally were developed for numerical data can be applied to any types of measurement levels by using nonlinear PCA. Sparseness and joint dimension reduction and clustering for nonlinear data, the results of recent studies, are extensions obtained by the same matrix operations in nonlinear PCA. Finally, an acceleration algorithm is proposed to reduce the problem of computational cost in the ALS iteration in nonlinear multivariate methods. This book thus presents the usefulness of nonlinear PCA which can be applied to different measurement levels data in diverse fields. As well, it covers the latest topics including the extension of the traditional statistical method, newly proposed nonlinear methods, and computational efficiency in the methods.

About the authors

Yuichi Mori, Professor, Okayama University of Science Masahiro Kuroda Professor, Okayama University of Science

Reviews

“This book endeavors to demonstrate the usefulness of theory and applications of the nonlinear PCA and MCA. The authors have written an interesting and high valuable book, which gives an excellent overview to the mathematical foundations and the statistical principles of its themes. At the end of each chapter, a short list of references is provided and this will help a reader wishing to pursue this area further.” (Apostolos Batsidis, zbMATH, Vol. 1366.62011, 2017)


Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook 46,00 €
price for Spain (gross)
  • ISBN 978-981-10-0159-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 57,19 €
price for Spain (gross)
  • ISBN 978-981-10-0157-4
  • Free shipping for individuals worldwide. COVID-19 shipping restrictions apply.
  • Immediate ebook access, if available*, with your print order
  • Usually ready to be dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Nonlinear Principal Component Analysis and Its Applications
Authors
Series Title
JSS Research Series in Statistics
Copyright
2016
Publisher
Springer Singapore
Copyright Holder
The Author(s)
eBook ISBN
978-981-10-0159-8
DOI
10.1007/978-981-10-0159-8
Softcover ISBN
978-981-10-0157-4
Series ISSN
2364-0057
Edition Number
1
Number of Pages
X, 80
Number of Illustrations
9 b/w illustrations, 8 illustrations in colour
Topics

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