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Constrained Principal Component Analysis and Related Techniques

Yoshio Takane
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A01=Yoshio Takane
advanced data analysis
Author_Yoshio Takane
bootstrap for reliability assessment
Canonical Correspondence Analysis
Category=JMB
Category=PBT
computer software for CPCA
Confidence Regions
constrained principal component analysis (CPCA)
constrained regression for multivariate analysis
correspondence
CPCA
cross-validation methods for fine-tuning the values of regularization parameters
data
Data Matrix
Data Set
different constraints on different dimensions (DCDD)
dimension reduction strategies
disturbance
eq_bestseller
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
eq_non-fiction
eq_society-politics
Functional PCA
Generalized Eigenequation
Iv Estimator
LS Criterion
matrix
Mimic Model
Missing Data
Moore Penrose Inverse
multivariate data analysis
Multivariate Data Matrix
multivariate statistical methods
Orthogonal Procrustes Rotation
Orthogonal Projector
Partial RA
permutation tests for dimensionality selection
Pi Ci
predictor
projection and singular value decomposition
projection techniques
QR Decomposition
Reduced Rank Approximations
regression techniques and principal component analysis
Ridge Estimator
Robust PCA
scores
Separate PCAs
singular
singular value decomposition
Singular Vectors
Square Root Factors
statistical modeling applications
terms
Total SS
value
variables

Product details

  • ISBN 9780367576288
  • Weight: 640g
  • Dimensions: 156 x 234mm
  • Publication Date: 30 Jun 2020
  • Publisher: Taylor & Francis Ltd
  • Publication City/Country: GB
  • Product Form: Paperback
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Description

In multivariate data analysis, regression techniques predict one set of variables from another while principal component analysis (PCA) finds a subspace of minimal dimensionality that captures the largest variability in the data.



  • How can regression analysis and PCA be combined in a beneficial way?


  • Why and when is it a good idea to combine them?


  • What kind of benefits are we getting from them?


Addressing these questions, Constrained Principal Component Analysis and Related Techniques shows how constrained PCA (CPCA) offers a unified framework for these approaches.

The book begins with four concrete examples of CPCA that provide readers with a basic understanding of the technique and its applications. It gives a detailed account of two key mathematical ideas in CPCA: projection and singular value decomposition. The author then describes the basic data requirements, models, and analytical tools for CPCA and their immediate extensions. He also introduces techniques that are special cases of or closely related to CPCA and discusses several topics relevant to practical uses of CPCA. The book concludes with a technique that imposes different constraints on different dimensions (DCDD), along with its analytical extensions. MATLAB® programs for CPCA and DCDD as well as data to create the book’s examples are available on the author’s website.
About Yoshio Takane

Yoshio Takane is an emeritus professor at McGill University and an adjunct professor at the University of Victoria. He is a former president of the Psychometric Society and a recipient of a Career Award from the Behaviormetric Society of Japan and a Special Award from the Japanese Psychological Association. His recent interests include regularization techniques for multivariate data analysis, acceleration methods for iterative model fitting, the development of structural equation models for analyzing brain connectivity, and various kinds of singular value decompositions. He earned his DL from the University of Tokyo and PhD from the University of North Carolina at Chapel Hill.

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