# PCA - Principal Component Analysis (PCA) Modified from a...

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Principal Component Analysis (PCA) Modified from a similar description originally written by Ann Noble PCA is used to a. reduce a large number of correlated variables and to replace them with a smaller set of uncorrelated variables. b. understand the relationships among the original variables. c. understand the relative importance of the original variables d. understand the relationships among the objects and the original variables e. see groups in the objects or to see outlier objects. To determine the principal components (PCs) the eigen values and eigen vectors of the correlation (or covariance) matrix are calculated. If the variables are measured in different units then the correlation matrix must be used, since it standardizes the data. For sensory descriptive data (where all evaluations are done using the same scale) we usually use the covariance matrix. It is possible to do PCA in SAS, MINITAB, UNSCRAMBLER, etc. The first PC is extracted to account for the maximum amount of variance in the data space. It is therefore a line that goes through the plane of maximum elongation. The second PC is extracted to account for the maximum amount of remaining variance in the data space and to be orthogonal (or uncorrelated or at a 90° degree angle) to the first PC. Graphically, this PC is perpendicular to the first PC. The process is repeated until the total number of PCs has

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## This note was uploaded on 09/29/2010 for the course VEN 91863 taught by Professor Hildergardheymann during the Spring '09 term at UC Davis.

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PCA - Principal Component Analysis (PCA) Modified from a...

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