Effect of Centereing Data in Principal Component Analysis

ABSTRACT: In the analysis of multivariate data, the processing and extracting meaningful results becomes very difficult due large number of variables and data. Therefore, statistical techniques to deal with such data, by finding linear combinations of existing variables, such that each variable is assigned a coefficient or score that determines its contribution to that linear combination. These linear combinations are called Principal Components (PC) and the methodology used in the determination of the PCs is called Principal Component Analysis (PCA). In general the number of PCs is expected to be the same as the number of variables. However, the PCs are determined such that the great percentage of variation (usually over 90%) in the data accumulates in the first few PCs. Then, the remaining PCs become redundant, and the information contained in a large number of variables is reduced into a few new variables (PCs) that are linear combinations of original variables. Therefore, a technique used in determining the PCs is very important. In this work, theory of PCA with related mathematical background is explained and using a certain data set, various ways of the application of PCA technique is investigated, obtained results are interpreted. Keywords: Principle component analysis, data, eigenvalue, eigenvector, covariance, correlation, standardized data, centered data. …………………………………………………………………………………………………………………………