Part of the Master of Science Thesis by D.P.
Original Research Article
Weighted analysis of principal components: Two approximations to statistical weights†
Article first published online: 30 MAR 2005
Copyright © 1992 John Wiley & Sons Ltd.
Journal of Chemometrics
Volume 6, Issue 5, pages 257–266, September/October 1992
How to Cite
Simeon, V. and Pavković, D. (1992), Weighted analysis of principal components: Two approximations to statistical weights. J. Chemometrics, 6: 257–266. doi: 10.1002/cem.1180060505
- Issue published online: 30 MAR 2005
- Article first published online: 30 MAR 2005
- Manuscript Accepted: 22 JUL 1992
- Manuscript Received: 1 NOV 1991
- Principal factor analysis;
- Factor analysis;
- Eigenvalue analysis;
- Multivariate analysis;
- Weighted factor analysis;
- Procrustean analysis
Two approximate methods for weighted principal components analysis (WPCA) were devised and tested in numerical experiments using either empirical variances (obtained from replicated data) or assumed variances (derived from unreplicated data). In the first (‘spherical’) approximation each data vector was assigned a weight proportional to the geometrical mean of its variances in all dimensions. The arithmetical mean of variances was used instead in the other approximation. Both the numerical experiments with artificial data containing random errors of various kinds (constant, proportional, constant plus proportional, Poisson) and the analysis of two sets of Raman spectra clearly indicated the necessity of introducing statistical weights. The spherical approximation was found to be slightly better than the arithmetical one. The application of statistical weighting was found to improve the performance of PCA in estimation problems.