Experimental comparison of data transformation procedures for analysis of principal components.

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).

[1]  T J Spinks,et al.  Generation of myocardial factor images directly from the dynamic oxygen-15-water scan without use of an oxygen-15-carbon monoxide blood-pool scan. , 1998, Journal of nuclear medicine : official publication, Society of Nuclear Medicine.

[2]  Jeanne Fine,et al.  Asymptotic study of the multivariate functional model in the case of a random number of observations for each mean , 1994 .

[3]  I. Buvat,et al.  A statistical model for the determination of the optimal metric in factor analysis of medical image sequences (FAMIS) , 1993 .

[4]  J. Ashburner,et al.  Linear dimension reduction of sequences of medical images: II. Direct sum decomposition , 1995, Physics in medicine and biology.

[5]  J. E. Jackson.  A User's Guide to Principal Components , 1991 .

[6]  P. Hannequin,et al.  The determination of the number of statistically significant factors in factor analysis of dynamic structures , 1989 .

[7]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .

[8]  A. Pousse,et al.  Asympotic study of the multivariate functional model. application to the metric choice in principal component analysis , 1992 .

[9]  K. Jöreskog,et al.  Applied Factor Analysis in the Natural Sciences. , 1997 .

[10]  H. BERGMANN,et al.  Hybrid phantoms for testing the measurement of regional dynamics in dynamic renal scintigraphy , 1998, Nuclear medicine communications.

[11]  A A Lammertsma,et al.  Linear dimension reduction of sequences of medical images: III. Factor analysis in signal space. , 1996, Physics in medicine and biology.

[12]  A A Lammertsma,et al.  Linear dimension reduction of sequences of medical images: I. Optimal inner products. , 1995, Physics in medicine and biology.

[13]  J. P. Bazin,et al.  Handling of Dynamic Sequences in Nuclear Medicine , 1982, IEEE Transactions on Nuclear Science.

[14]  P. Bandettini,et al.  Synthetic images by subspace transforms. I. Principal components images and related filters. , 1994, Medical physics.

[15]  Calyampudi R. Rao,et al.  Linear Statistical Inference and Its Applications. , 1975 .

[16]  D. Barber.  The use of principal components in the quantitative analysis of gamma camera dynamic studies. , 1980, Physics in medicine and biology.

[17]  M Sámal,et al.  Rotation to simple structure in factor analysis of dynamic radionuclide studies. , 1987, Physics in medicine and biology.

[18]  C. R. Rao,et al.  Linear Statistical Inference and its Applications , 1968 .