Feature reduction via generalized uncorrelated linear discriminant analysis

IEEE Transactions on Knowledge and Data Engineering

Volumn 18, Issue 10, 2006, Pages 1312-1322

  Ye, Jieping ^a,b   Janardan, Ravi ^a,c   Li, Qi ^a,d   Park, Haesun ^e  

^a IEEE   (United States)

^b Arizona State University   (United States)

^c UNIVERSITY OF MINNESOTA   (United States)

^d University of Delaware   (United States)

^e Georgia Institute of Technology   (United States)

Author keywords

Feature reduction; Generalized singular value decomposition; QR decomposition; Uncorrelated linear discriminant analysis

Indexed keywords

FEATURE REDUCTION; GENERALIZED SINGULAR VALUE DECOMPOSITION; QR-DECOMPOSITION; UNCORRELATED LINEAR DISCRIMINANT ANALYSIS;

ALGORITHMS; DATA MINING; KNOWLEDGE ENGINEERING; OPTIMIZATION; PARAMETER ESTIMATION; STATISTICAL METHODS;

FEATURE EXTRACTION;

EID: 33748336501     PISSN: 10414347     EISSN: None     Source Type: Journal    
DOI: 10.1109/TKDE.2006.160     Document Type: Article

References (31)

1. P. Belhumeour, J. Hespanha, and D. Kriegman, "Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 7, pp. 711-720, 1997.
2. M. Berry, S. Dumais, and G. O'Brie, "Using Linear Algebra for Intelligent Information Retrieval," SIAM Rev., vol. 37, pp. 573-595, 1995.
3. L. Chen, H. Liao, M. Ko, J. Lin, and G. Yu, "A New LDA-Based Face Recognition System Which Can Solve the Small Sample Size Problem," Pattern Recognition, vol. 33, pp. 1713-1726, 2000.
4. S. Deerwester, S. Dumais, G. Furnas, T. Landauer, and R. Harshman, "Indexing by Latent Semantic Analysis," J. Soc. for Information Science, vol. 41, pp. 391-407, 1990.
5. L. Duchene and S. Leclerq, "An Optimal Transformation for Discriminant and Principal Component Analysis," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 10, no. 6, pp. 978-983, 1988.
6. R. Duda, P. Hart, and D. Stork, Pattern Classification. Wiley, 2000.
7. S. Dudoit, J. Fridlyand, and T.P. Speed, "Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data," J. Am. Statistical Assoc., vol. 97, no. 457, pp. 77-87, 2002.
8. D. Foley and J. Sammon, "An Optimal Set of Discriminant Vectors," IEEE Trans. Computers, vol. 24, no. 3, pp. 281-289, 1975.
9. J. Friedman, "Regularized Discriminant Analysis," J. Am. Statistical Assoc., vol. 84, no. 405, pp. 165-175, 1989.
10. K. Fukunaga, Introduction to Statistical Pattern Classification.Academic Press, 1990.
11. G.H. Golub and C.F. Van Loan, Matrix Computations, third ed. The Johns Hopkins Univ. Press, 1996.
12. T. Hastie, A. Buja, and R. Tibshirani, "Penalized Discriminant Analysis," Annals of Statistics, vol. 23, pp. 73-102, 1995.
13. T. Hastie and R. Tibshirani, "Discriminant Analysis by Gaussian Mixtures," J. Royal Statistical Soc. series B, vol. 58, pp. 158-176, 1996.
14. T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer, 2001.
15. P. Howland, M. Jeon, and H. Park, "Structure Preserving Dimension Reduction for Clustered Text Data Based on the Generalized Singular Value Decomposition," SIAM J. Matrix Analysis and Applications, vol. 25, no. 1, pp. 165-179, 2003.
16. P. Howland and H. Park, "Generalizing Discriminant Analysis Using the Generalized Singular Value Decomposition," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 8, pp. 995-1006, Aug. 2004.
17. Z. Jin, J.Y. Yang, Z.-S. Hu, and Z. Lou, "Face Recognition Based on the Uncorrelated Discriminant Transformation," Pattern Recognition, vol. 34, pp. 1405-1416, 2001.
18. Z. Jin, J.-Y. Yang, Z.-M. Tang, and Z.-S. Hu, "A Theorem on the Uncorrelated Optimal Discriminant Vectors," Pattern Recognition, vol. 34, no. 10, pp. 2041-2047, 2001.
19. I.T. Jolliffe, Principal Component Analysis. Springer-Verlag, 1986.
20. W. Krzanowski, P. Jonathan, W. McCarthy, and M. Thomas, "Discriminant Analysis with Singular Covariance Matrices: Methods and Applications to Spectroscopic Data," Applied Statistics, vol. 44, pp. 101-115, 1995.
21. C. Paige and M. Saunders, "Towards a Generalized Singular Value Decomposition," SIAM J. Numerical Analysis, vol. 18, pp. 398-405, 1981.
22. H. Park, M. Jeon, and J. Rosen, "Lower Dimensional Representation of Text Data Based on Centroids and Least Squares," BIT Numerical Math., vol. 43, no. 2, pp. 1-22, 2003.
23. S. Ramaswamy et al., "Multiclass Cancer Diagnosis Using Tumor Gene Expression Signatures," Proc. Nat'l Academy of Science, vol. 98, no. 26, pp. 15149-15154, 2001.
24. B. Schökopf and A. Smola, Learning with Kernels: Support Vector Machines, Regularization, Optimization and Beyond. MIT Press, 2002.
25. D.L. Swets and J. Weng, "Using Discriminant Eigenfeatures for Image Retrieval," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, no. 8, pp. 831-836, Aug. 1996.
26. M. Turk and A. Pentland, "Face Recognition Using Eigenfaces," Proc. Computer Vision and Pattern Recognition Conf., pp. 586-591, 1991.
27. V. Vapnik, Statistical Learning Theory. Wiley, 1998.
28. J. Ye, "Characterization of a Family of Algorithms for Generalized Discriminant Analysis on Undersampled Problems," J. Machine Learning Research, vol. 6, pp. 483-502, 2005.
29. J. Ye, R. Janardan, C. Park, and H. Park, "An Optimization Criterion for Generalized Discriminant Analysis on Undersampled Problems," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 8, pp. 982-994, Aug. 2004.
30. C.H. Yeang et al., "Molecular Classification of Multiple Tumor Types," Bioinformatics, vol. 17, no. 1, pp. 1-7, 2001.
31. E.J. Yeoh et al., "Classification, Subtype Discovery, and Prediction of Outcome in Pediatric Lymphoblastic Leukemia by Gene Expression Profiling," Cancer Cell, vol. 1, no. 2, pp. 133-143, 2002.