A Correlation Rank Determinator for Princip al Components

A new statistic, defined as Ro(k) = s(k)/ -.Jsr+ ... + sE {s(k) denoting the k-th singular value of data matrix}, is proposed for assessing the significance of individual components in principal-components analysis (PCA). Ro was shown to be the correlation coefficient of the prediction from the k-th principal component to the original data. The common significance test on Ro was applied as a semiempirical determinator of the effective rank (»pseudorank«) of data matrices. By examining the performance of this simple test on Ro on a number of data matrices ofknown effective ranks (UVNis and Raman spectra of aqueous solutions of various inorganic salts), it was shown to be a serious competitor to the rank determinators commonly used in PCA.