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Nonlinear Principal Component Analysis and Its Applications (Paperback, 1st ed. 2016)
Loot Price: R1,829
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Nonlinear Principal Component Analysis and Its Applications (Paperback, 1st ed. 2016)
Series: JSS Research Series in Statistics
Expected to ship within 18 - 22 working days
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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.
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