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Principal Component Analysis

In: An Introduction to Statistical Data Science

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  • Giorgio Picci

    (University of Padua, Department of Information Engineering)

Abstract

In this chapter we discuss some general techniques for statistical data compression (or noise reduction). These techniques can be used for the purpose of feature extraction in decision problems and have acquired a great importance in applications to classification. A couple of such significant applications will be briefly illustrated. There is also a large body of applications of the underlying compression idea to regression problems. The second part of the chapter could be described as “reduced-data” regression and goes under the name of Canonical Correlation Analysis which has a deep statistical significance. We analyze it both from a probabilistic perspective and from an algorithmic viewpoint.

Suggested Citation

  • Giorgio Picci, 2024. "Principal Component Analysis," Springer Books, in: An Introduction to Statistical Data Science, chapter 7, pages 273-305, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-66619-3_7
    DOI: 10.1007/978-3-031-66619-3_7
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