Statistical mechanics of learning orthogonal signals for general covariance models

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2010, Issue 4, 2010, Pages

  Hoyle, David C ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

Analysis of algorithms; Data mining (theory); Typical case computational complexity

Indexed keywords

EID: 77951692617     PISSN: 17425468     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2010/04/P04009     Document Type: Article

References (24)

1. Engel A and Van den Broeck C 2001 Statistical Mechanics of Learning (Cambridge: Cambridge University Press)
2. Biehl M 1994 An exactly solvable model of unsupervised learning Europhys. Lett. 25 391 (Pubitemid 24763899)
3. Reimann P, Van den Broeck C and Bex G J 1996 A Gaussian scenario for unsupervised learning J. Phys. A: Math. Gen. 29 3521 (Pubitemid 126088717)
4. Joliffe I T 1986 Principal Component Analysis (New York: Springer)
5. Hoyle D C and Rattray M 2004 Principal-component-analysis eigenvalue spectra from data with symmetry-breaking structure Phys. Rev. E 69 026124
6. Hoyle D C and Rattray M 2007 Statistical mechanics of learning multiple orthogonal signals: asymptotic theory and fluctuation effects Phys. Rev. E 75 016101
7. Johnstone I M 2001 On the distribution of the largest eigenvalue in principal components analysis Ann. Stat. 29 295
8. Johnstone I M 2006 High dimensional statistical inference and random matrices Preprint arXiv:math/0611589v1 [math.ST]
9. Mezard M, Parisi G and Virasoro M 1987 Spin Glass Theory and Beyond (Singapore: World Scientific)
10. Anderson T W 1963 Asymptotic theory for principal component analysis Ann. Math. Stat. 34 122
11. Paul D 2007 Asymptotics of sample eigenstruture for a large dimensional spiked covariance model Stat. Sin. 17 1617
12. Hoyle D C and Rattray M 2003 PCA learning for sparse high-dimensional data Europhys. Lett. 62 117 (Pubitemid 36420421)
13. Baik J, Ben Arous G and Peche S 2005 Phase transition of the largest eigenvalue for non-null complex sample covariance matrices Ann. Probab. 33 1643 (Pubitemid 41560766)
14. Baik J and Silverstein J W 2006 Eigenvalues of large sample covariance matrices of spiked population models J. Multivar. Anal. 97 1382 (Pubitemid 43705671)
15. Marenko V A and Pastur L A 1967 Distribution of eigenvalues for some sets of random matrices Math. USSR-Sb 1 457
16. Wachter K W 1978 The strong limits of random matrix spectra for sample matrices of independent elements Ann. Probab. 6 1
17. Sengupta A M and Mitra P P 1999 Distributions of singular values for some random matrices Phys. Rev. E 60 3389
18. Hoyle D C and Rattray M 2004 A statistical mechanics analysis of Gram matrix eigenvalue spectra Proc. COLT'04, Conf. on Learning Theory (Banff, 2004) (Lecture Notes in Artificial Intelligence 3120) ed J Shawe-Taylor and Y Singer (Berlin: Springer) p579
19. El Karoui N 2008 Spectrum estimation for large dimensional covariance matrices using random matrix theory Ann. Stat. 36 2757
20. Urbanczik R 2003 Statistical physics of independent component analysis Europhys. Lett. 64 564 (Pubitemid 37398598)
21. Bai Z D 1999 Methodologies in spectral analysis of large dimensional random matrices, a review Stat. Sin. 9 611
22. Rider P R 1957 Generalized cauchy distributions Ann. Inst. Stat. Math. 9 215
23. Miller J H and Thomas J B 1972 Detectors for discrete-time signals in non-Gaussian noise IEEE Trans. Inform. Theory 18 241
24. Hoyle D C 2008 Automatic PCA dimension selection for high dimensional data and small sample sizes J. Mach. Learn. Res. 9 2733