Nonlinear Principal Component Analysis and Its Applications

Yuichi Mori, Masahiro Kuroda, Naomichi Makino (Autoren)

Buch | Softcover

80 Seiten

2016 | 1st ed. 2016
Springer Verlag, Singapore
978-981-10-0157-4 (ISBN)

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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.

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

1. Introduction.- 2. Nonlinear Principal Component Analysis.- 3. Application.

Erscheinungsdatum	06.01.2017
Reihe/Serie	JSS Research Series in Statistics
Reihe/Serie	SpringerBriefs in Statistics
Zusatzinfo	8 Illustrations, color; 9 Illustrations, black and white; X, 80 p. 17 illus., 8 illus. in color.
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Computerprogramme / Computeralgebra
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
	Sozialwissenschaften ► Soziologie ► Empirische Sozialforschung
Schlagworte	Alternating Least Squares • Mixed Measurement Level Data • Multiple Correspondence Analysis • Nonlinear PCA • Optimal Scaling
ISBN-10	981-10-0157-X / 981100157X
ISBN-13	978-981-10-0157-4 / 9789811001574
Zustand	Neuware