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Volumn 52, Issue 1, 2007, Pages 423-437

Improving implementation of linear discriminant analysis for the high dimension/small sample size problem

Author keywords

Dimension reduction; Linear discriminant analysis; Numerical aspects of FLDA; Small sample size problem; Sparsity

Indexed keywords

COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; FUNCTION EVALUATION; PROBLEM SOLVING; SAMPLING;

EID: 34548273742     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2007.02.001     Document Type: Article
Times cited : (37)

References (30)
  • 2
    • 34548225695 scopus 로고    scopus 로고
    • Bai, Z., Demmel, J., Dongarra, J., Ruhe, A., van der Vorst, H. (Eds.), 2000. Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide, 2000, SIAM, Philadelphia.
  • 3
    • 0030326891 scopus 로고    scopus 로고
    • Regularized Gaussian discriminant analysis through eigenvalue decomposition
    • Bensmail H., and Celeux G. Regularized Gaussian discriminant analysis through eigenvalue decomposition. J. Amer. Statist. Assoc. 91 (1996) 1743-1748
    • (1996) J. Amer. Statist. Assoc. , vol.91 , pp. 1743-1748
    • Bensmail, H.1    Celeux, G.2
  • 4
    • 0034300875 scopus 로고    scopus 로고
    • A new LDA-based face recognition system which can solve the small sample size problem
    • Chen L.-F., Liao H.-Y.M., Ko M.-T., Lin J.-C., and Yu G.-J. A new LDA-based face recognition system which can solve the small sample size problem. Pattern Recognition 33 10 (2000) 1713-1726
    • (2000) Pattern Recognition , vol.33 , Issue.10 , pp. 1713-1726
    • Chen, L.-F.1    Liao, H.-Y.M.2    Ko, M.-T.3    Lin, J.-C.4    Yu, G.-J.5
  • 5
    • 0026746940 scopus 로고
    • Optimal Fisher discriminant analysis using the rank decomposition
    • Cheng Y.-Q., Zhuang Y.-M., and Yang J.-Y. Optimal Fisher discriminant analysis using the rank decomposition. Pattern Recognition 25 1 (1992) 101-111
    • (1992) Pattern Recognition , vol.25 , Issue.1 , pp. 101-111
    • Cheng, Y.-Q.1    Zhuang, Y.-M.2    Yang, J.-Y.3
  • 7
    • 0000764772 scopus 로고
    • The use of multiple measurements in taxonomic problems
    • Fisher R.A. The use of multiple measurements in taxonomic problems. Ann. Eugenics 7 (1936) 179-188
    • (1936) Ann. Eugenics , vol.7 , pp. 179-188
    • Fisher, R.A.1
  • 8
    • 84887916087 scopus 로고
    • Regularized discriminant analysis
    • Friedman J.H. Regularized discriminant analysis. J. Amer. Statist. Assoc. 84 (1989) 165-175
    • (1989) J. Amer. Statist. Assoc. , vol.84 , pp. 165-175
    • Friedman, J.H.1
  • 10
    • 0346034995 scopus 로고    scopus 로고
    • A generalized Foley-Sammon transform based on generalized Fisher discriminant criterion and its application to face recognition
    • Guo Y.-F., Li S.-J., Yang J.-Y., Shu T.-T., and Wu L.-D. A generalized Foley-Sammon transform based on generalized Fisher discriminant criterion and its application to face recognition. Pattern Recognition Lett. 24 (2003) 147-158
    • (2003) Pattern Recognition Lett. , vol.24 , pp. 147-158
    • Guo, Y.-F.1    Li, S.-J.2    Yang, J.-Y.3    Shu, T.-T.4    Wu, L.-D.5
  • 11
    • 34548271827 scopus 로고    scopus 로고
    • Hastie, T., Tibshirani, R., 2003. Expression arrays and the p ≫ n problem. See 〈http://www-stat.stanford.edu/∼hastie/Papers/pgtn.pdf〉.
  • 12
    • 0030189750 scopus 로고    scopus 로고
    • Covariance matrix estimation and classification with limited training data
    • Hoffbeck J.P., and Landgrebe D.A. Covariance matrix estimation and classification with limited training data. IEEE Trans. Pattern Anal. Mach. Intell. 18 7 (1996) 763-767
    • (1996) IEEE Trans. Pattern Anal. Mach. Intell. , vol.18 , Issue.7 , pp. 763-767
    • Hoffbeck, J.P.1    Landgrebe, D.A.2
  • 13
    • 0025792756 scopus 로고
    • Optimal discriminant plane for a small number of samples and design method of classifier on the plane
    • Hong Z.-Q., and Yang J.-Y. Optimal discriminant plane for a small number of samples and design method of classifier on the plane. Pattern Recognition 24 4 (1991) 317-324
    • (1991) Pattern Recognition , vol.24 , Issue.4 , pp. 317-324
    • Hong, Z.-Q.1    Yang, J.-Y.2
  • 14
    • 3242707002 scopus 로고    scopus 로고
    • Generalizing discriminant analysis using the generalized singular value decomposition
    • Howland P., and Park H. Generalizing discriminant analysis using the generalized singular value decomposition. IEEE Trans. Pattern Anal. Mach. Intell. 26 8 (2004) 995-1006
    • (2004) IEEE Trans. Pattern Anal. Mach. Intell. , vol.26 , Issue.8 , pp. 995-1006
    • Howland, P.1    Park, H.2
  • 15
    • 1342310014 scopus 로고    scopus 로고
    • Structure preserving dimension reduction for clustered text data based on the generalized singular value decomposition
    • Howland P., Jeon M., and Park H. Structure preserving dimension reduction for clustered text data based on the generalized singular value decomposition. SIAM J. Matrix Anal. Appl. 25 1 (2003) 165-179
    • (2003) SIAM J. Matrix Anal. Appl. , vol.25 , Issue.1 , pp. 165-179
    • Howland, P.1    Jeon, M.2    Park, H.3
  • 16
    • 27744565938 scopus 로고    scopus 로고
    • Solving the small sample size problem in face recognition using generalized discriminant analysis
    • Howland P., Wang J., and Park H. Solving the small sample size problem in face recognition using generalized discriminant analysis. Pattern Recognition 39 (2006) 277-287
    • (2006) Pattern Recognition , vol.39 , pp. 277-287
    • Howland, P.1    Wang, J.2    Park, H.3
  • 18
    • 21844475661 scopus 로고    scopus 로고
    • Dimension reduction in text classification with support vector machines
    • Kim H., Howland P., and Park P. Dimension reduction in text classification with support vector machines. J. Mach. Learn. Res. 6 (2005) 37-53
    • (2005) J. Mach. Learn. Res. , vol.6 , pp. 37-53
    • Kim, H.1    Howland, P.2    Park, P.3
  • 19
    • 21844512674 scopus 로고
    • Discriminant analysis with singular covariance matrices: methods and applications to spectroscopic data
    • Krzanowski W.J., Jonathan P., McCarthy W.V., and Thomas M.R. Discriminant analysis with singular covariance matrices: methods and applications to spectroscopic data. Appl. Statist. 44 1 (1995) 101-115
    • (1995) Appl. Statist. , vol.44 , Issue.1 , pp. 101-115
    • Krzanowski, W.J.1    Jonathan, P.2    McCarthy, W.V.3    Thomas, M.R.4
  • 20
    • 84957354433 scopus 로고    scopus 로고
    • Effective implementation of linear discriminant analysis for face recognition and verification
    • Leonardis A., and Solina F. (Eds), Springer, Berlin
    • Li Y., Kittler J., and Matas J. Effective implementation of linear discriminant analysis for face recognition and verification. In: Leonardis A., and Solina F. (Eds). Lecture Notes in Computer Science 1689 (1999), Springer, Berlin 234-242
    • (1999) Lecture Notes in Computer Science 1689 , pp. 234-242
    • Li, Y.1    Kittler, J.2    Matas, J.3
  • 21
    • 34548283796 scopus 로고    scopus 로고
    • MathWorks, Inc., 1984-2005. MATLAB 7.0, 〈http://www.mathworks.com/products/matlab/〉.
  • 22
    • 0000356673 scopus 로고
    • An algorithm for generalized matrix eigenvalue problems
    • Moler C.B., and Stewart G.W. An algorithm for generalized matrix eigenvalue problems. SIAM J. Numer. Anal. 10 2 (1973) 241-256
    • (1973) SIAM J. Numer. Anal. , vol.10 , Issue.2 , pp. 241-256
    • Moler, C.B.1    Stewart, G.W.2
  • 23
    • 0001129014 scopus 로고
    • Towards a generalized singular value decomposition
    • Paige C.C., and Saunders M.A. Towards a generalized singular value decomposition. SIAM J. Numer. Anal. 18 3 (1981) 398-405
    • (1981) SIAM J. Numer. Anal. , vol.18 , Issue.3 , pp. 398-405
    • Paige, C.C.1    Saunders, M.A.2
  • 25
    • 34548213398 scopus 로고    scopus 로고
    • R Development Core Team, 2005. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna.
  • 27
    • 0037076272 scopus 로고    scopus 로고
    • Diagnosis of multiple cancer types by shrunken centroids of gene expression
    • Tibshirani R., Hastie T., Narasimhan B., and Chu G. Diagnosis of multiple cancer types by shrunken centroids of gene expression. Proc. Nat. Acad. Sci. USA 99 10 (2002) 6567-6572
    • (2002) Proc. Nat. Acad. Sci. USA , vol.99 , Issue.10 , pp. 6567-6572
    • Tibshirani, R.1    Hastie, T.2    Narasimhan, B.3    Chu, G.4
  • 29
    • 0036487285 scopus 로고    scopus 로고
    • Why can LDA be performed in PCA transformed space?
    • Yang J., and Yang J.-Y. Why can LDA be performed in PCA transformed space?. Pattern Recognition 36 2 (2003) 563-566
    • (2003) Pattern Recognition , vol.36 , Issue.2 , pp. 563-566
    • Yang, J.1    Yang, J.-Y.2
  • 30
    • 34548217468 scopus 로고    scopus 로고
    • Yang, J., Yu, H., Kunz, W., 2000. An efficient LDA algorithm for face recognition. Sixth International Conference on Control, Automation, Robotics and Vision (ICARCV2000).


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.