TY - JOUR
T1 - Experimental comparison of data transformation procedures for analysis of principal components
AU - Šámal, Martin
AU - Kárný, Miroslav
AU - Benali, Habib
AU - Backfrieder, Werner
AU - Todd-Pokropek, Andrew
AU - Bergmann, Helmar
PY - 1999/11
Y1 - 1999/11
N2 - 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).
AB - 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).
KW - Computer Simulation
KW - Image Processing, Computer-Assisted
KW - Models, Theoretical
KW - Normal Distribution
KW - Nuclear Medicine/methods
KW - Phantoms, Imaging
KW - Poisson Distribution
KW - Reproducibility of Results
UR - http://www.scopus.com/inward/record.url?scp=0344672460&partnerID=8YFLogxK
U2 - 10.1088/0031-9155/44/11/310
DO - 10.1088/0031-9155/44/11/310
M3 - Article
C2 - 10588287
AN - SCOPUS:0344672460
SN - 0031-9155
VL - 44
SP - 2821
EP - 2834
JO - Physics in Medicine and Biology
JF - Physics in Medicine and Biology
IS - 11
ER -