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Principal Components Analysis - CMU Statistics

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.

components: the kth principal component is the leading component of the residu-als after subtracting off the first k − 1 components. In practice, it is faster to use eigenvector-solvers to get all the components at once from v, but this idea is correct in principle. This is a good place to remark that if the data really fall in a q ...

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