Rank selection in noisy PCA with sure and random matrix theory

ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

Volumn , Issue , 2008, Pages 3317-3320

  Ulfarsson, M O ^a   Solo, V ^b  

^a UNIVERSITY OF ICELAND   (Iceland)

^b UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Model order selection; Principal component analysis; Random matrix theory; Stein's unbiased risk estimator (SURE)

Indexed keywords

ACOUSTICS; FINANCIAL DATA PROCESSING; RANDOM PROCESSES; RISK ASSESSMENT; RISK PERCEPTION; SIGNAL PROCESSING; SPEECH;

INTERNATIONAL CONFERENCES; MODEL ORDER SELECTION; RANDOM MATRIX THEORY; STEIN'S UNBIASED RISK ESTIMATOR (SURE);

PRINCIPAL COMPONENT ANALYSIS;

EID: 51449107795     PISSN: 15206149     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ICASSP.2008.4518360     Document Type: Conference Paper

References (23)

1. I. Jolliffe, Principal Component Analysis, 2nd ed. New York, NY: Springer, 2002.
2. D. Lawley, "A modified method of estimation in factor analysis and some large sample results," in Uppsala symposium on psychological factor analysis, Uppsala, Sweden, 1953, pp. 35-42.
3. P. Stoica and Y. Selen, "Model-order selection. A review of information criterion rules," IEEE Signal Proc. Mag., vol. 21, no. 4, pp. 36-47, 2004.
4. R. Preisendorfer, Principal Component Analysis in Meteorlogy and Oceangraphy. Amsterdam, Holland: Elsevier, 1988.
5. J. Ramsay and B. Silverman, Functional Data Analysis, 1st ed. New York, NY: Springer, 1997.
6. M. Ulfarsson and V. Solo, "Smooth principal component analysis with application to functional magnetic resonance imaging," in Proc. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP'06), vol. 2, Toulouse, France, May 2006, pp. II - 993 - II - 996.
7. T. Minka, "Automatic choice of dimensionality for PCA," in Advances in Neural Information Processing Systems (NIPS'00), 2000, pp. 598-604.
8. C. Beckmann and S. Smith, "Probabilistic independent component analysis for functional magnetic resonance imaging," IEEE Trans. Med. Imag, vol. 23, no. 2, 2004.
9. A. Seghouane and A. Cichocki, "Bayesian estimation of the number of principal components," Signal Processing, vol. 87, pp. 562-568, 2007.
10. C. Stein, "Estimation of the mean of a multivariate normal distribution," Ann. Stat., vol. 9, no. 6, pp. 1135-1151, 1981.
11. D. Donoho and I. Johnstone, "Ideal spatial adaptation by wavelet shrinkage," Biometrika, vol. 81, no. 3, pp. 425-455, 1994.
12. M. Hudson, "Maximum likelihood restoration and choice of smoothing parameter in deconvolution of image data subject to Poisson noise," Comput Stat Data Anal, vol. 26, no. 4, pp. 393-410, 1998.
13. V. Solo, "A sure-fired way to choose smoothing parameters in ill-conditioned inverse problems," in Proc. IEEE International Conference on Image Processing (ICIP'96), vol. 3, Lausanne, Switzerland, 1996, pp. 89-92.
14. C. Theobald, "An inequality with application to multivariate analysis," Biometrika, vol. 62, no. 2, pp. 461-466, 1975.
15. M. Tipping and C. Bishop, "Probabilistic principal component analysis," J. Royal Stat. Soc., Series B, vol. 61, no. 3, pp. 611-622, 1999.
16. R. Kass and A. Raftery, "Bayes factors," J. Amer. Stat. Assoc., vol. 90, no. 430, pp. 773-795, 1995.
17. T. Anderson, "Estimating linear statistical relationships," Ann. Statist., vol. 12, no. 1, pp. 1-45, 1984.
18. V. Marcenko and L. Pastur, "Distribution of eigenvalues of some sets of random matrices," Math. USSR-Sb., vol. 1, pp. 507-536, 1967.
19. I. Johnstone, "On the distribution of the largest eigenvalue in principal component analysis," Annals Stat., vol. 29, no. 2, pp. 295-327, 2001.
20. R. Everson and S. Roberts, "Inferring the eigenvalues of co-variance matrices from limited, noisy data," IEEE Trans. Signal Proc., vol. 48, no. 7, pp. 2083-2091, 2000.
21. J. Silverstein and P. Combettes, "Signal detection via spectral theory of large dimensional random matrices," IEEE Trans. Signal Proc., vol. 40, no. 8, 1992.
22. J. Baik and J. Silverstein, "Eigenvalues of large sample covariance matrices of spiked population models," J. Multivariate Anal., vol. 97, pp. 1382-1408, 2006.
23. D. Paul, "Asymptotics of the leading sample eigenvalues for a spiked covariance model," Department of Statistic, Stanford University, Tech. Rep., 2004.