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Principal Component Analysis

In: Applied Multivariate Statistical Analysis

Author

Listed:
  • Wolfgang Karl Härdle

    (Humboldt-Universität zu Berlin, Ladislaus von Bortkiewicz Chair of Statistics)

  • Léopold Simar

    (Université Catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences)

  • Matthias R. Fengler

    (University of St. Gallen, School of Economics and Political Science)

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.

Suggested Citation

  • Wolfgang Karl Härdle & Léopold Simar & Matthias R. Fengler, 2024. "Principal Component Analysis," Springer Books, in: Applied Multivariate Statistical Analysis, edition 0, chapter 0, pages 309-345, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-63833-6_11
    DOI: 10.1007/978-3-031-63833-6_11
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