Principal Component Analysis

Wolfgang Karl Härdle, Leopold Simar and Matthias Fengler
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Wolfgang Karl Härdle: Humboldt-Universität zu Berlin, Ladislaus von Bortkiewicz Chair of Statistics

Chapter Chapter 11 in Applied Multivariate Statistical Analysis, 2024, pp 309-345 from Springer

Abstract: Abstract Chapter 10 presented the basic geometric tools needed to produce a lower-dimensional description of the rows and columns of a multivariate data matrix. Principal component analysis has the same objective with the exception that the rows of the data matrix X $${{\mathcal {X}}}$$ will now be considered as observations from a p-variate random variable X $${X}$$ . The principal idea of reducing the dimension of X $${X}$$ is achieved through linear combinations. Low-dimensional linear combinations are often easier to interpret and serve as an intermediate step in a more complex data analysis. More precisely one looks for linear combinations which create the largest spread among the values of X. In other words, one is searching for linear combinations with the largest variances.

Date: 2024
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Related works:
Chapter: Principal Components Analysis (2019)
Chapter: Principal Components Analysis (2015)
Chapter: Principal Components Analysis (2003)
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DOI: 10.1007/978-3-031-63833-6_11

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