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 (R) programs for CPCA and DCDD as well as data
to create the book's examples are available on the author's
website.
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