an introduction to Principal Component Analysis (PCA)

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abstract Principal component analysis (PCA) is a technique that is useful for the compression and classification of data. The purpose is to reduce the dimensionality of a data set (sample) by finding a new set of variables, smaller than the original set of variables, that nonetheless retains most of the sample's information. By information we mean the variation present in the sample, given by the correlations between the original variables. The new variables, called principal components (PCs), are uncorrelated, and are ordered by the fraction of the total information each retains.
overview • geometric picture of PCs • algebraic definition and derivation of PCs • usage of PCA • astronomical application
Page 1: an introduction to Principal Compon
Page 5 and 6: Geometric picture of principal comp
Page 7 and 8: Algebraic definition of PCs Likewis
Page 9 and 10: Algebraic derivation of coefficient
Page 11 and 12: Algebraic derivation of coefficient
Page 13 and 14: Algebraic formulation of PCA Given
Page 15 and 16: usage of PCA: Probability distribut
Page 17 and 18: usage of PCA: Inference about popul
Page 19 and 20: usage of PCA: Practical computation
Page 21 and 22: usage of PCA: Data compression Beca
Page 23 and 24: astronomical application: PCs for e
Page 25: eferences Connolly, and Szalay, et

an introduction to Principal Component Analysis (PCA)

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