Sparse linear discriminant analysis with applications to high dimensional low sample size data

IAENG International Journal of Applied Mathematics

Volumn 39, Issue 1, 2009, Pages

  Qiao, Zhihua ^a   Zhou, Lan ^b   Huang, Jianhua Z ^b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Classification; Linear discriminant analysis; Regularization; Sparse LDA; Variable selection

Indexed keywords

EID: 61849100967     PISSN: 19929978     EISSN: 19929986     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. Ahn, J. and Marron, J.S., 2007, The maximal data piling direction for discrimination, manuscript.
2. Alon, U., Barkai, N., Notterman, D., Gish, K., Mack, S. and Levine, J., 1999, Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by ologonucleotide arrays, Proc. Natl. Acad. Sci, USA, 96, 503-511.
3. Campbell, N.A., 1980, Shrunken estimator in discriminant and canonical variate analysis, Applied Statistics, 29, 5-14.
4. Cliff, N., 1966, Orthogonal rotation to congruence. Psychometrika, 31, 33-42.
5. Efron B., Hastie T., Johnstone, I., and Tibshirani, R., 2004, Least angle regression, Ann. Statist., 32, 407-499.
6. Fisher, R. A., 1936, The use of multiple measurements in taxonomic problems. Ann. Eugen, 7, 179-188.
7. Friedman, J. H., 1989, Regularized discriminant analysis, Journal of the American Statistical Association, 84, 165-175.
8. Gower, J. C. and Dijksterhuis, G. B., 2004, Procrustes Problems, Oxford University Press, New York.
9. Hotelling, H., 1933, Analysis of a complex of statistical variables into principal components. J. Educ. Psych., 24, 417-441, 498-520.
10. Hotelling, H., 1936, Relations between two sets of variates, Biometrika, 28, 321-377.
11. Fukunaga, K., 1990, Introduction to Statistical Pattern Classification. Academic Press, San Diego, California, USA, 1990.
12. Mardia, K.V., Kent, J.T. and Bibby J.M., 1979, Multivariate analysis, Academic Press.
13. Marron, J. S., Todd, M. and Ahn, J., 2007, Distance weighted discrimination, Journal of American Statistical Association, 102, 1267-1271.
14. Pearson, K., 1901, On lines and planes of closest fit to systems of points in space, Philosophical Magazine, 2, 559-572.
15. Peck, R. and Van Ness, J., 1982, The use of shrinkage estimators in linear discriminant analysis, IEEE Transactions on Pattern Analysis and Machine Intelligence, 4, 531-537.
16. Rayens, W.S., 1990, A Role for covariance stabilization in the construction of the classical mixture surface, Journal of Chemometrics, 4, 159-169.
17. Singh, D., Febbo, P. G., Ross, K., Jackson, D. G., Manola, J., Ladd, C., Tamayo, P., Renshaw, A. A., D'Amico, A.V., Richie, J. P., Lander, E. S., Loda, M., Kantoff, P.,W., Golub, T. R., and Sellers,W. R., 2002, Gene expression correlates of clinical prostate cancer behavior, Cancer Cell, 1, 203-209.
18. Tibshirani, R., 1996, Regression shrinkage and selection via the lasso, Journal of the Royal Statistical Society, Series B, 58, 267-288.
19. Ye, J., 2005, Characterization of a family of algorithms for generalized discriminant analysis on undersampled problems, Journal of Machine Learning Research, 6, 483-502.
20. Ye, J., Janardan, R., Li, Q. and Park H., 2006, Feature reduction via generalized uncorrelated linear discriminant analysis, emphIEEE Transactions on Knowledge and Data Engineering, 18, 1312-1322.
21. Zou, H., Hastie, T. and Tibshirani, R., 2006, Sparse principal component analysis, Journal of Computational and Graphical Statistics, 15, 157-177.