Experimental comparison of data transformation procedures for analysis of principal components

Martin Šámal, Miroslav Kárný, Habib Benali, Werner Backfrieder, Andrew Todd-Pokropek, Helmar Bergmann

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)

Abstract

Results of principal component analysis depend on data scaling. Recently, based on theoretical considerations, several data transformation procedures have been suggested in order to improve the performance of principal component 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, and to compare several procedures for data transformation in analysis of principal components experimentally. The experiment was performed with simulated data and the performance of individual procedures was compared using the non-parametric Friedman's test. The optimum scaling found was that which unifies the variance of noise in the observed images. In data with a Poisson distribution, the optimum scaling was the norm used in correspondence analysis. Scaling mainly affected the definition of the signal space. Once the dimension of the signal space was known, the differences in error of data and signal reproduction were small. The choice of data transformation depends on the amount of available prior knowledge (level of noise in individual images, number of components, etc), on the type of noise distribution (Gaussian, uniform, Poisson, other), and on the purpose of analysis (data compression, filtration, feature extraction).

Original languageEnglish
Pages (from-to)2821-2834
Number of pages14
JournalPhysics in Medicine and Biology
Volume44
Issue number11
DOIs
Publication statusPublished - Nov 1999
Externally publishedYes

Keywords

  • Computer Simulation
  • Image Processing, Computer-Assisted
  • Models, Theoretical
  • Normal Distribution
  • Nuclear Medicine/methods
  • Phantoms, Imaging
  • Poisson Distribution
  • Reproducibility of Results

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