A Correlation Rank Determinator for Principal Components
Damir Pavković, Vladislav Tomišić, Revik Nuss, Vladimir Simeon · University of Zagreb University Computing Centre (SRCE) · 1996
A new statistic, defined as Ro(k) = s(k)/ -.Js r + ... + 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.