Effective PCA for high-dimension, low-sample-size data with noise reduction via geometric representations

Journal of Multivariate Analysis

Volumn 105, Issue 1, 2012, Pages 193-215

  Yata, Kazuyoshi ^a   Aoshima, Makoto ^a  

^a UNIVERSITY OF TSUKUBA   (Japan)

Author keywords

Consistency; Discriminant analysis; Eigenvalue distribution; Geometric representation; HDLSS; Inverse matrix; Noise reduction; Primary; Principal component analysis; Secondary

Indexed keywords

EID: 80053531107     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2011.09.002     Document Type: Article

References (16)

1. Ahn J., Marron J.S., Muller K.M., Chi Y.-Y. The high-dimension, low-sample-size geometric representation holds under mild conditions. Biometrika 2007, 94:760-766.
2. Baik J., Ben Arous G., Péché S. Phase transition of the largest eigenvalue for non-null complex covariance matrices. Ann. Probab. 2005, 33:1643-1697.
3. Baik J., Silverstein J.W. Eigenvalues of large sample covariance matrices of spiked population models. J. Multivariate Anal. 2006, 97:1382-1408.
4. Bradley R.C. Basic properties of strong mixing conditions. A survey and some open questions. Probab. Surv. 2005, 2:107-144. (electronic).
5. Hall P., Marron J.S., Neeman A. Geometric representation of high dimension, low sample size data. J. R. Stat. Soc. Ser. B 2005, 67:427-444.
6. Johnstone I. On the distribution of the largest eigenvalue in principal components analysis. Ann. Statist. 2001, 29:295-327.
7. Jung S., Marron J.S. PCA consistency in high dimension, low sample size context. Ann. Statist. 2009, 37:4104-4130.
8. Kolmogorov A.N., Rozanov Y.A. On strong mixing conditions for stationary Gaussian processes. Theory Probab. Appl. 1960, 5:204-208.
9. Lee S., Zou F., Wright F.A. Convergence and prediction of principal component scores in high-dimensional settings. Ann. Statist. 2010, 38:3605-3629.
10. Paul D. Asymptotics of sample eigenstructure for a large dimensional spiked covariance model. Statist. Sinica 2007, 17:1617-1642.
11. Srivastava M.S. Minimum distance classification rules for high dimensional data. J. Multivariate Anal. 2006, 97:2057-2070.
12. Srivastava M.S. Multivariate theory for analyzing high dimensional data. J. Japan Statist. Soc. 2007, 37:53-86.
13. Srivastava M.S., Kubokawa T. Comparison of discrimination methods for high dimensional data. J. Japan Statist. Soc. 2007, 37:123-134.
14. Yata K., Aoshima M. PCA consistency for non-gaussian data in high dimension, low sample size context. Comm. Statist. Theory Methods 2009, 38:2634-2652.
15. Yata K., Aoshima M. Effective PCA for high-dimension, low-sample-size data with singular value decomposition of cross data matrix. J. Multivariate Anal. 2010, 101:2060-2077.
16. Yata K., Aoshima M. Intrinsic dimensionality estimation of high dimension, low sample size data with d-asymptotics. Comm. Statist. Theory Methods 2010, 39:1511-1521.