Original scientific paper

A Correlation Rank Determinator for Principal Components

Damir Pavković ; Laboratory of Physical Chemistry, Faculty of Science, University of Zagreb, 10000 Zagreb, P.O. Box 163, Croatia
Vladislav Tomišić ; Laboratory of Physical Chemistry, Faculty of Science, University of Zagreb, 10000 Zagreb, P.O. Box 163, Croatia
Revik Nuss ; Laboratory of Physical Chemistry, Faculty of Science, University of Zagreb, 10000 Zagreb, P.O. Box 163, Croatia
Vladimir Simeon ; Laboratory of Physical Chemistry, Faculty of Science, University of Zagreb, 10000 Zagreb, P.O. Box 163, Croatia

Abstract

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.

Keywords

Hrčak ID:

177137

URI

https://hrcak.srce.hr/177137

Publication date:

1.11.1996.

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