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Erschienen in:
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2018 | OriginalPaper | Buchkapitel

6. Principal Component Analysis and Extensions

verfasst von : Patrick Mair

Erschienen in: Modern Psychometrics with R

Verlag: Springer International Publishing

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Abstract

This chapter introduces principal component analysis (PCA), a technique for dimension reduction in multivariate datasets. At its core there is a matrix decomposition technique called singular value decomposition, which is introduced at the beginning of this chapter. This is followed by PCA model formulation, computation, and an application. Relationships with exploratory factor analysis are discussed as well. Subsequently, some PCA variants such as robust and sparse PCA are briefly discussed. The final two sections introduce two extensions of PCA. The first one is three-way PCA for three-way input data structures. The second one is called independent component analysis and illustrated using electroencephalography (EEG) data.

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Vorheriges Kapitel Preference Modeling
Nächstes Kapitel Correspondence Analysis
Fußnoten
1
For readers who are more attracted to a sonic introduction to SVD rather than a formal one, Michael Greenacre composed an SVD song (“It had to be U”), available on YouTube.
 
2
In this section we follow a notation for indices of the data and components as well as the number of them which is different from that used before but which is standard in the literature of three-way analysis (see Kiers, 2000).
 
3
We omit the matrix formulation for all three-way PCA models since it requires some 3D matrix operations that are beyond scope of this book (see, e.g., Kroonenberg, 2008, for corresponding expressions).
 
4
Biplots are introduced in more detail in Chap. 10.
 
5
Thanks for Hrag Pailian for sharing this dataset.
 
Literatur
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Metadaten
Titel
Principal Component Analysis and Extensions
verfasst von
Patrick Mair
Copyright-Jahr
2018
Buch
Modern Psychometrics with R

Print ISBN: 978-3-319-93175-3

Electronic ISBN: 978-3-319-93177-7

Copyright-Jahr: 2018

DOI
https://doi.org/10.1007/978-3-319-93177-7_6

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