메뉴 건너뛰기




Volumn 24, Issue 8, 2015, Pages 2382-2392

Worst case linear discriminant analysis as scalable semidefinite feasibility problems

Author keywords

Dimensionality Reduction; Semidefinite Programming; Worst Case Linear Discriminant Analysis

Indexed keywords

DISCRIMINANT ANALYSIS; NEWTON-RAPHSON METHOD;

EID: 84929484948     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2015.2401511     Document Type: Article
Times cited : (9)

References (50)
  • 2
    • 33749257955 scopus 로고    scopus 로고
    • Distance metric learning for large margin nearest neighbor classification
    • Cambridge, MA, USA: MIT Press
    • K. Q. Weinberger, J. Blitzer, and L. K. Saul, "Distance metric learning for large margin nearest neighbor classification," in Advances in Neural Information Processing Systems, vol. 18. Cambridge, MA, USA: MIT Press, 2006, pp. 1473-1481.
    • (2006) Advances in Neural Information Processing Systems , vol.18 , pp. 1473-1481
    • Weinberger, K.Q.1    Blitzer, J.2    Saul, L.K.3
  • 3
    • 0034300875 scopus 로고    scopus 로고
    • A new LDA-based face recognition system which can solve the small sample size problem
    • L.-F. Chen, H.-Y. M. Liao, M.-T. Ko, J.-C. Lin, and G.-J. Yu, "A new LDA-based face recognition system which can solve the small sample size problem," Pattern Recognit., vol. 33, no. 10, pp. 1713-1726, 2000.
    • (2000) Pattern Recognit. , 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
  • 4
    • 21844447839 scopus 로고    scopus 로고
    • Characterization of a family of algorithms for generalized discriminant analysis on undersampled problems
    • Apr.
    • J. Ye, "Characterization of a family of algorithms for generalized discriminant analysis on undersampled problems," J. Mach. Learn. Res., vol. 6, no. 4, pp. 483-502, Apr. 2005.
    • (2005) J. Mach. Learn. Res. , vol.6 , Issue.4 , pp. 483-502
    • Ye, J.1
  • 5
    • 85162035389 scopus 로고    scopus 로고
    • Worst-case linear discriminant analysis
    • Cambridge, MA, USA: MIT Press
    • Y. Zhang and D.-Y. Yeung, "Worst-case linear discriminant analysis," in Advances in Neural Information Processing Systems, vol. 23. Cambridge, MA, USA: MIT Press, 2010, pp. 2568-2576.
    • (2010) Advances in Neural Information Processing Systems , vol.23 , pp. 2568-2576
    • Zhang, Y.1    Yeung, D.-Y.2
  • 6
    • 84861833031 scopus 로고    scopus 로고
    • Enhanced Fisher discriminant criterion for image recognition
    • Q. Gao, J. Liu, J. Zhang, J. Hou, and X. Yang, "Enhanced Fisher discriminant criterion for image recognition," Pattern Recognit., vol. 45, no. 10, pp. 3717-3724, 2012.
    • (2012) Pattern Recognit. , vol.45 , Issue.10 , pp. 3717-3724
    • Gao, Q.1    Liu, J.2    Zhang, J.3    Hou, J.4    Yang, X.5
  • 9
    • 79953054794 scopus 로고    scopus 로고
    • Max-min distance analysis by using sequential SDP relaxation for dimension reduction
    • May
    • W. Bian and D. Tao, "Max-min distance analysis by using sequential SDP relaxation for dimension reduction," IEEE Trans. Pattern Anal. Mach. Intell., vol. 33, no. 5, pp. 1037-1050, May 2011.
    • (2011) IEEE Trans. Pattern Anal. Mach. Intell. , vol.33 , Issue.5 , pp. 1037-1050
    • Bian, W.1    Tao, D.2
  • 10
    • 84908681002 scopus 로고    scopus 로고
    • Asymptotic generalization bound of Fisher's linear discriminant analysis
    • W. Bian and D. Tao, "Asymptotic generalization bound of Fisher's linear discriminant analysis," IEEE Trans. Pattern Anal. Mach. Intell., vol. 36, no. 12, pp. 2325-2337, 2014.
    • (2014) IEEE Trans. Pattern Anal. Mach. Intell. , vol.36 , Issue.12 , pp. 2325-2337
    • Bian, W.1    Tao, D.2
  • 12
    • 33745743918 scopus 로고    scopus 로고
    • Computational and theoretical analysis of null space and orthogonal linear discriminant analysis
    • Jul.
    • J. Ye and T. Xiong, "Computational and theoretical analysis of null space and orthogonal linear discriminant analysis," J. Mach. Learn. Res., vol. 7, pp. 1183-1204, Jul. 2006.
    • (2006) J. Mach. Learn. Res. , vol.7 , pp. 1183-1204
    • Ye, J.1    Xiong, T.2
  • 13
    • 67349282310 scopus 로고    scopus 로고
    • Trace ratio problem revisited
    • Apr.
    • Y. Jia, F. Nie, and C. Zhang, "Trace ratio problem revisited," IEEE Trans. Neural Netw., vol. 20, no. 4, pp. 729-735, Apr. 2009.
    • (2009) IEEE Trans. Neural Netw. , vol.20 , Issue.4 , pp. 729-735
    • Jia, Y.1    Nie, F.2    Zhang, C.3
  • 14
    • 0346034995 scopus 로고    scopus 로고
    • A generalized Foley-Sammon transform based on generalized Fisher discriminant criterion and its application to face recognition
    • Y.-F. Guo, S.-J. Li, J.-Y. Yang, T.-T. Shu, and L.-D. Wu, "A generalized Foley-Sammon transform based on generalized Fisher discriminant criterion and its application to face recognition," Pattern Recognit. Lett., vol. 24, nos. 1-3, pp. 147-158, 2003.
    • (2003) Pattern Recognit. Lett. , vol.24 , Issue.1-3 , pp. 147-158
    • Guo, Y.-F.1    Li, S.-J.2    Yang, J.-Y.3    Shu, T.-T.4    Wu, L.-D.5
  • 17
    • 79954475526 scopus 로고    scopus 로고
    • Trace optimization and eigenproblems in dimension reduction methods
    • E. Kokiopoulou, J. Chen, and Y. Saad, "Trace optimization and eigenproblems in dimension reduction methods," Numer. Linear Algebra Appl., vol. 18, no. 3, pp. 565-602, 2011.
    • (2011) Numer. Linear Algebra Appl. , vol.18 , Issue.3 , pp. 565-602
    • Kokiopoulou, E.1    Chen, J.2    Saad, Y.3
  • 18
    • 84879571292 scopus 로고    scopus 로고
    • Distance metric learning, with application to clustering with side-information
    • Cambridge, MA, USA: MIT Press
    • E. P. Xing, A. Y. Ng, M. I. Jordan, and S. Russell, "Distance metric learning, with application to clustering with side-information," in Advances in Neural Information Processing Systems, vol. 15. Cambridge, MA, USA: MIT Press, 2003, pp. 505-512.
    • (2003) Advances in Neural Information Processing Systems , vol.15 , pp. 505-512
    • Xing, E.P.1    Ng, A.Y.2    Jordan, M.I.3    Russell, S.4
  • 19
    • 61749090884 scopus 로고    scopus 로고
    • Distance metric learning for large margin nearest neighbor classification
    • Feb.
    • K. Q. Weinberger and L. K. Saul, "Distance metric learning for large margin nearest neighbor classification," J. Mach. Learn. Res., vol. 10, pp. 207-244, Feb. 2009.
    • (2009) J. Mach. Learn. Res. , vol.10 , pp. 207-244
    • Weinberger, K.Q.1    Saul, L.K.2
  • 20
    • 49449103684 scopus 로고    scopus 로고
    • Supervised dimensionality reduction via sequential semidefinite programming
    • C. Shen, H. Li, and M. J. Brooks, "Supervised dimensionality reduction via sequential semidefinite programming," Pattern Recognit., vol. 41, no. 12, pp. 3644-3652, 2008.
    • (2008) Pattern Recognit. , vol.41 , Issue.12 , pp. 3644-3652
    • Shen, C.1    Li, H.2    Brooks, M.J.3
  • 22
    • 33646249113 scopus 로고    scopus 로고
    • Least-squares covariance matrix adjustment
    • S. Boyd and L. Xiao, "Least-squares covariance matrix adjustment," SIAM J. Matrix Anal. Appl., vol. 27, no. 2, pp. 532-546, 2005.
    • (2005) SIAM J. Matrix Anal. Appl. , vol.27 , Issue.2 , pp. 532-546
    • Boyd, S.1    Xiao, L.2
  • 23
    • 14544268199 scopus 로고    scopus 로고
    • A dual approach to semidefinite least-squares problems
    • J. Malick, "A dual approach to semidefinite least-squares problems," SIAM J. Matrix Anal. Appl., vol. 26, no. 1, pp. 272-284, 2004.
    • (2004) SIAM J. Matrix Anal. Appl. , vol.26 , Issue.1 , pp. 272-284
    • Malick, J.1
  • 24
    • 77951274410 scopus 로고    scopus 로고
    • A Newton-CG augmented Lagrangian method for semidefinite programming
    • X.-Y. Zhao, D. Sun, and K.-C. Toh, "A Newton-CG augmented Lagrangian method for semidefinite programming," SIAM J. Optim., vol. 20, no. 4, pp. 1737-1765, 2010.
    • (2010) SIAM J. Optim. , vol.20 , Issue.4 , pp. 1737-1765
    • Zhao, X.-Y.1    Sun, D.2    Toh, K.-C.3
  • 25
    • 84861325244 scopus 로고    scopus 로고
    • Calibrating least squares covariance matrix problems with equality and inequality constraints
    • Y. Gao and D. Sun, "Calibrating least squares covariance matrix problems with equality and inequality constraints," SIAM J. Matrix Anal. Appl., vol. 31, no. 3, pp. 1432-1457, 2009.
    • (2009) SIAM J. Matrix Anal. Appl. , vol.31 , Issue.3 , pp. 1432-1457
    • Gao, Y.1    Sun, D.2
  • 26
    • 70450197241 scopus 로고    scopus 로고
    • Robust stochastic approximation approach to stochastic programming
    • A. Nemirovski, A. Juditsky, G. Lan, and A. Shapiro, "Robust stochastic approximation approach to stochastic programming," SIAM J. Optim., vol. 19, no. 4, pp. 1574-1609, 2009.
    • (2009) SIAM J. Optim. , vol.19 , Issue.4 , pp. 1574-1609
    • Nemirovski, A.1    Juditsky, A.2    Lan, G.3    Shapiro, A.4
  • 27
    • 79952297247 scopus 로고    scopus 로고
    • Alternating direction augmented Lagrangian methods for semidefinite programming
    • Z. Wen, D. Goldfarb, and W. Yin, "Alternating direction augmented Lagrangian methods for semidefinite programming," Math. Program. Comput., vol. 2, nos. 3-4, pp. 203-230, 2010.
    • (2010) Math. Program. Comput. , vol.2 , Issue.3-4 , pp. 203-230
    • Wen, Z.1    Goldfarb, D.2    Yin, W.3
  • 29
    • 84955457109 scopus 로고    scopus 로고
    • Efficient low-rank stochastic gradient descent methods for solving semidefinite programs
    • J. Chen, T. Yang, and S. Zhu, "Efficient low-rank stochastic gradient descent methods for solving semidefinite programs," in Proc. Int. Workshop Artif. Intell. Statist., 2014, pp. 122-130.
    • (2014) Proc. Int. Workshop Artif. Intell. Statist. , pp. 122-130
    • Chen, J.1    Yang, T.2    Zhu, S.3
  • 33
    • 84860670539 scopus 로고    scopus 로고
    • Positive semidef-inite metric learning using boosting-like algorithms
    • C. Shen, J. Kim, L. Wang, and A. Van Den Hengel, "Positive semidef-inite metric learning using boosting-like algorithms," J. Mach. Learn. Res., vol. 13, no. 1, pp. 1007-1036, 2012.
    • (2012) J. Mach. Learn. Res. , vol.13 , Issue.1 , pp. 1007-1036
    • Shen, C.1    Kim, J.2    Wang, L.3    Hengel Den A.Van4
  • 34
    • 0039907084 scopus 로고
    • On the sum of the largest eigenvalues of a symmetric matrix
    • M. L. Overton and R. S. Womersley, "On the sum of the largest eigenvalues of a symmetric matrix," SIAM J. Matrix Anal. Appl., vol. 13, no. 1, pp. 41-45, 1992.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , Issue.1 , pp. 41-45
    • Overton, M.L.1    Womersley, R.S.2
  • 37
    • 77957300831 scopus 로고    scopus 로고
    • Projection methods for conic feasibility problems: Applications to polynomial sum-of-squares decompositions
    • D. Henrion and J. Malick, "Projection methods for conic feasibility problems: Applications to polynomial sum-of-squares decompositions," Optim. Methods Softw., vol. 26, no. 1, pp. 23-46, 2011.
    • (2011) Optim. Methods Softw. , vol.26 , Issue.1 , pp. 23-46
    • Henrion, D.1    Malick, J.2
  • 38
    • 0031345518 scopus 로고    scopus 로고
    • Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization
    • C. Zhu, R. H. Byrd, P. Lu, and J. Nocedal, "Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization," ACM Trans. Math. Softw., vol. 23, no. 4, pp. 550-560, 1997.
    • (1997) ACM Trans. Math. Softw. , vol.23 , Issue.4 , pp. 550-560
    • Zhu, C.1    Byrd, R.H.2    Lu, P.3    Nocedal, J.4
  • 39
    • 84855220977 scopus 로고    scopus 로고
    • Remark on 'Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound constrained optimization'
    • J. L. Morales and J. Nocedal, "Remark on 'Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound constrained optimization'," ACM Trans. Math. Softw., vol. 38, no. 1, p. 7, 2011.
    • (2011) ACM Trans. Math. Softw. , vol.38 , Issue.1 , pp. 7
    • Morales, J.L.1    Nocedal, J.2
  • 40
    • 0033295027 scopus 로고    scopus 로고
    • SDPT3-A MATLAB software package for semidefinite programming, version 1.3
    • K. C. Toh, M. J. Todd, and R. H. Tütüncü, "SDPT3-A MATLAB software package for semidefinite programming, version 1.3," Optim. Methods Softw., vol. 11, nos. 1-4, pp. 545-581, 1999.
    • (1999) Optim. Methods Softw. , vol.11 , Issue.1-4 , pp. 545-581
    • Toh, K.C.1    Todd, M.J.2    Tütüncü, R.H.3
  • 41
    • 0033296299 scopus 로고    scopus 로고
    • Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones
    • J. F. Sturm, "Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones," Optim. Methods Softw., vol. 11, nos. 1-4, pp. 625-653, 1999.
    • (1999) Optim. Methods Softw. , vol.11 , Issue.1-4 , pp. 625-653
    • Sturm, J.F.1
  • 42
    • 78649934709 scopus 로고    scopus 로고
    • School Inf. Comput. Sci., Univ. California, Irvine, CA, USA
    • A. Frank and A. Asuncion. (2010). UCI Machine Learning Repository. School Inf. Comput. Sci., Univ. California, Irvine, CA, USA. [Online]. Available: http://archive.ics.uci.edu/ml
    • (2010) UCI Machine Learning Repository
    • Frank, A.1    Asuncion, A.2
  • 43
    • 0028734063 scopus 로고
    • Parameterisation of a stochastic model for human face identification
    • Dec.
    • F. S. Samaria and A. C. Harter, "Parameterisation of a stochastic model for human face identification," in Proc. 2nd IEEE Workshop Appl. Comput. Vis., Dec. 1994, pp. 138-142.
    • (1994) Proc. 2nd IEEE Workshop Appl. Comput. Vis , pp. 138-142
    • Samaria, F.S.1    Harter, A.C.2
  • 44
    • 0031185845 scopus 로고    scopus 로고
    • Eigenfaces vs. Fisherfaces: Recognition using class specific linear projection
    • Jul.
    • P. N. Belhumeur, J. P. Hespanha, and D. Kriegman, "Eigenfaces vs. Fisherfaces: Recognition using class specific linear projection," IEEE Trans. Pattern Anal. Mach. Intell., vol. 19, no. 7, pp. 711-720, Jul. 1997.
    • (1997) IEEE Trans. Pattern Anal. Mach. Intell. , vol.19 , Issue.7 , pp. 711-720
    • Belhumeur, P.N.1    Hespanha, J.P.2    Kriegman, D.3
  • 45
    • 0347380229 scopus 로고    scopus 로고
    • The CMU pose, illumination, and expression database
    • T. Sim, S. Baker, and M. Bsat, "The CMU pose, illumination, and expression database," IEEE Trans. Pattern Anal. Mach. Intell., vol. 25, no. 12, pp. 1615-1618, 2003.
    • (2003) IEEE Trans. Pattern Anal. Mach. Intell. , vol.25 , Issue.12 , pp. 1615-1618
    • Sim, T.1    Baker, S.2    Bsat, M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.