A CORRELATION RANK DETERMINATOR FOR PRINCIPAL COMPONENTS

A new statistic, defined as R(0)(k) = s(k)/root s2/1+...+s2/b {s(k) de noting the k-th singular value of data matrix}, is proposed for assess ing the significance of individual components in principal-components analysis (PCA). R(0) was shown to be the correlation coefficient of th e prediction from the h-th principal component to the original data. T he common significance test on R(0) was applied as a semiempirical det erminator of the effective rank (''pseudorank'') of data matrices. By examining the performance of this simple test on R(0) on a number of d ata matrices of known effective ranks (UV/Vis and Raman spectra of aqu eous solutions of various inorganic salts), it was shown to be a serio us competitor to the rank determinators commonly used in PCA.