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Principal Components Analysis - Carnegie Mellon University

Chapter 18 Principal Components AnalysisPrincipal Components Analysis (PCA) is one of a family of techniques for takinghigh-dimensional data, and using the dependencies between the variables to representit in a more tractable, lower-dimensional form, without losing too much is one of the simplest and most robust ways of doing suchdimensionalityreduction. It is also one of the oldest, and has been rediscovered many times inmany fields, so it is also known as the Karhunen-Lo ve transformation, the Hotellingtransformation, the method of empirical orthogonal functions, and singular valuedecomposition1.

j=1 λ j (18.21) just as the R2 of a linear regression is the fraction of the original variance of the dependent variable kept by the fitted values. 2Exception: if n< p, there are only distinct eigenvectors and eigenvalues.

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