Experimental comparison of data transformation procedures for analysis of principal components

Results of principal component analysis depend on data scaling. Recently, b ased on theoretical considerations, several data transformation procedures have been suggested in order to improve the performance of principal compon ent analysis of image data with respect to the optimum separation of signal and noise. The aim of this study was to test some of those suggestions, an d to compare several procedures for data transformation in analysis of prin cipal components experimentally. The experiment was performed with simulate d data and the performance of individual procedures was compared using the non-parametric Friedman's test. The optimum scaling found was that which un ifies the variance of noise in the observed images. In data with a Poisson distribution, the optimum scaling was the norm used in correspondence analy sis. Scaling mainly affected the definition of the signal space. Once the d imension of the signal space was known, the differences in error of data an d signal reproduction were small. The choice of data transformation depends on the amount of available prior knowledge (level of noise in individual i mages, number of components, etc), on the type of noise distribution (Gauss ian, uniform, Poisson, other), and on the purpose of analysis (data compres sion, filtration, feature extraction).