Principal Component Analysis of Localization-Delocalization Matrices

Principal Component Analysis (PCA) and one of its variants, Factor Analysis (FA), are dimensionality reduction statistical approaches that replace the original correlated variables in a data set with fewer new ones that are linear combinations of the old ones. These new fewer variables capture the majority of the variability in the original data set and hence reduce or eliminate the redundancy of the row data. The new variables are uncorrelated, i.e., orthogonal, in PCA; or less correlated in the case of FA. If the original data set contains uncorrelated random variables, then PCA and FA become irrelevant since there is no data reduction possible in this case.