Supervised dimensionality reduction via sequential semidefinite programming

Pattern Recognition

Volumn 41, Issue 12, 2008, Pages 3644-3652

  Shen, Chunhua ^a,b   Li, Hongdong ^a,b   Brooks, Michael J ^c  

^a CSIRO   (Australia)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^c UNIVERSITY OF ADELAIDE   (Australia)

Author keywords

Dimensionality reduction; Linear discriminant analysis; Semidefinite programming

Indexed keywords

ARTIFICIAL INTELLIGENCE; DEMODULATION; LEARNING ALGORITHMS; LEARNING SYSTEMS; NONLINEAR PROGRAMMING; STANDARDS;

DIMENSIONALITY REDUCTION; DIMENSIONALITY REDUCTION ALGORITHMS; FACE DATA; GENERALIZED EIGENVALUE DECOMPOSITION; HANDWRITTEN DIGITS; LINEAR DISCRIMINANT ANALYSIS; MACHINE-LEARNING; OPTIMIZATION FRAMEWORK; OPTIMIZATION STRATEGIES; PROJECTION MATRICES; QUASI-LINEAR; SEMIDEFINITE OPTIMIZATION; SEMIDEFINITE PROGRAMMING; SPARSENESS CONSTRAINTS; SUPERVISED DIMENSIONALITY REDUCTION;

OPTIMIZATION;

EID: 49449103684     PISSN: 00313203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.patcog.2008.06.015     Document Type: Article

References (32)

1. Yan S., and Tang X. Trace quotient problems revisited. Proceedings of the European Conference on Computer Vision (2006), Springer, Berlin 232-244
2. Cai D., He X., Han J., and Zhang H.-J. Orthogonal Laplacianfaces for face recognition. IEEE Trans. Image Process. 15 11 (2006) 3608-3614
3. G. Hua, P.A. Viola, S.M. Drucker, Face recognition using discriminatively trained orthogonal rank one tensor projections, in: Proceedings of the IEEE Conference Computer Vision and Pattern Recognition, Minneapolis, MN, 2007.
4. J. Ye, T. Xiong, Null space versus orthogonal linear discriminant analysis, in: Proceedings of the International Conference on Machine Learning, Pittsburgh, PA, 2006, pp. 1073-1080.
5. Yang J., Yang J.-Y., and Zhang D. What's wrong with fisher criterion?. Pattern Recognition 35 11 (2002) 2665-2668
6. Boyd S., and Vandenberghe L. Convex Optimization (2004), Cambridge University Press, Cambridge
7. A. Ben-Tal, A.S. Nemirovski, Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, SIAM, Philadelphia, PA, USA, 2001.
8. Weinberger K.Q., and Saul L.K. Unsupervised learning of image manifolds by semidefinite programming. Int. J. Comput. Vision 70 1 (2006) 77-90
9. Keuchel J., Schnörr C., Schellewald C., and Cremers D. Binary partitioning, perceptual grouping, and restoration with semidefinite programming. IEEE Trans. Pattern Anal. Mach. Intell. 25 11 (2003) 1364-1379
10. Lanckriet G.R.G., Cristianini N., Bartlett P., Ghaoui L.E., and Jordan M.I. Learning the kernel matrix with semidefinite programming. J. Mach. Learn. Res. 5 (2004) 27-72
11. Overton M.L., and Womersley R.S. On the sum of the largest eigenvalues of a symmetric matrix. SIAM J. Matrix Anal. Appl. 13 1 (1992) 41-45
12. Overton M.L., and Womersley R.S. Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices. Math. Program. 62 1-3 (1993) 321-357
13. S. Agarwal, M. Chandraker, F. Kahl, S. Belongie, D.J. Kriegman, Practical global optimization for multiview geometry, in: Proceedings of the European Conference on Computer Vision, vol. 1, Graz, Austria, 2006, pp. 592-605.
14. Borchers B. CSDP, a C library for semidefinite programming. Optim. Methods Software 11 1 (1999) 613-623
15. Sturm J.F. Using SeDuMi 1.02, a matlab toolbox for optimization over symmetric cones (updated for version 1.05). Optim. Methods Software 11-12 (1999) 625-653
16. Schaible S. Fractional programming. II on Dinkelbach's algorithm. Manage. Sci. 22 8 (1976) 868-873
17. Yan S., Xu D., Zhang B., Zhang H., Yang Q., and Lin S. Graph embedding and extensions: a general framework for dimensionality reduction. IEEE Trans. Pattern Anal. Mach. Intell. 29 1 (2007) 40-51
18. R. Gilad-Bachrach, A. Navot, N. Tishby, Margin based feature selection-theory and algorithms, in: Proceedings of the International Conference on Machine Learning, Banff, Alberta, Canada, 2004.
19. R. Fransens, J. De Prins, L. Van Gool, SVM-based nonparametric discriminant analysis, an application to face detection, in: Proceedings of the IEEE International Conference on Computer Vision, vol. 2, Nice, France, 2003, pp. 1289-1296.
20. Li H., Jiang T., and Zhang K. Efficient and robust feature extraction by maximum margin criterion. IEEE Trans. Neural Network 17 1 (2006) 157-165
21. Xing E., Ng A., Jordan M., and Russell S. Distance metric learning with, application to clustering with side-information. Proceedings on Advances in Neural Information Processing System (2002), MIT Press, Cambridge, MA
22. K.Q. Weinberger, J. Blitzer, L.K. Saul, Distance metric learning for large margin nearest neighbor classification, in: Proceedings on Advances in Neural Information Processing System, 2005.
23. A. Globerson, S. Roweis, Metric learning by collapsing classes, in: Proceedings on Advances in Neural Information Processing System, 2005.
24. Goldberger J., Roweis S., Hinton G., and Salakhutdinov R. Neighbourhood component analysis. Proceedings on Advances in Neural Information Processing System (2004), MIT Press, Cambridge, MA
25. Belkin M., and Niyogi P. Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput. 15 6 (2003) 1373-1396
26. D. Newman, S. Hettich, C. Blake, C. Merz, UCI repository of machine learning databases (1998).
27. Jin Z., Yang J.-Y., Hu Z.-S., and Lou Z. Face recognition based on the uncorrelated discriminant transformation. Pattern Recognition 34 7 (2001) 1405-1416
28. M. Heiler, C. Schnorr, Learning non-negative sparse image codes by convex programming, in: Proceedings of the IEEE International Conference on Computer Vision, Beijing, China, 2005, pp. 1667-1674.
29. M. Heiler, C. Schnörr, Controlling sparseness in non-negative tensor factorization, in: Proceedings of the European Conference on Computer Vision, vol. 1, Graz, Austria, 2006, pp. 56-67.
30. Hoyer P.O. Non-negative matrix factorization with sparseness constraints. J. Mach. Learn. Res. 5 (2004) 1457-1469
31. d'Aspremont A., Ghaoui L.E., Jordan M.I., and Lanckriet G.R.G. A direct formulation for sparse PCA using semidefinite programming. SIAM Rev. 49 (2007) 434-448
32. Cadima J., and Jolliffe I. Loadings and correlations in the interpretation of principal components. Appl. Statist. 22 (1995) 203-214