Principal Components Analysis
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The basic aim of principal components analysis is to describe the variation in a set of correlated variables, x1, x2, ... x q in terms of a new set of uncorrelated variables, y1, y2, ... y q , each of which is a linear combination of the x variables. The new variables are derived in decreasing order of “importance” in the sense that y1 accounts for as much of the variation in the original data amongst all linear combinations of x1, x2, ... x q . Then y2 is chosen to account for as much as possible of the remaining variation, subject to being uncorrelated with y1, and so on. The new variables defined by this process, y1, y2, ... q q are the principal components.
KeywordsPrincipal Component Analysis Correlation Matrix Original Variable Principal Component Score Bivariate Data
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