A general exponential framework for dimensionality reduction

IEEE Transactions on Image Processing

Volumn 23, Issue 2, 2014, Pages 920-930

  Wang, Su Jing ^a,b   Yan, Shuicheng ^c   Yang, Jian ^d   Zhou, Chun Guang ^b   Fu, Xiaolan ^a  

^a INSTITUTE OF PSYCHOLOGY   (China)

^b JILIN UNIVERSITY   (China)

^c NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^d NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

dimensionality reduction; Face recognition; Laplacian embedding; manifold learning; matrix exponential

Indexed keywords

DIMENSIONALITY REDUCTION; LAPLACIANS; LOCALITY PRESERVING PROJECTIONS; LOW-DIMENSIONAL REPRESENTATION; MANIFOLD LEARNING; MATRIX EXPONENTIALS; PAIRWISE SIMILARITY MATRIX; SMALL SAMPLE SIZE PROBLEMS;

FACE RECOGNITION; LAPLACE TRANSFORMS;

ALGORITHMS;

EID: 84893086940     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2013.2297020     Document Type: Article

References (40)

1. F. De la Torre, "A least-squares framework for component analysis," IEEE Trans. Pattern Anal. Mach. Intell., vol. 34, no. 6, pp. 1041-1055, Jun. 2011.
2. M. Turk and A. Pentland, "Eigenfaces for recognition," J. Cognit. Neurosci., vol. 3, no. 1, pp. 71-86, 1991.
3. P. N. Belhumeur, J. P. Hespanha, and D. J. 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. (Pubitemid 127762263)
4. B. Moghaddam, "Principal manifolds and probabilistic subspaces for visual recognition," IEEE Trans. Pattern Anal. Mach. Intell., vol. 24, no. 6, pp. 780-788, Jun. 2002. (Pubitemid 34669591)
5. X. Wang and X. Tang, "A unified framework for subspace face recognition," IEEE Trans. Pattern Anal. Mach. Intell., vol. 26, no. 9, pp. 1222-1228, Sep. 2004.
6. 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 Recognit., vol. 33, no. 10, pp. 1713-1726, 2000.
7. J. Ye and Q. Li, "A two-stage linear discriminant analysis via QR-decomposition," IEEE Trans. Pattern Anal. Mach. Intell., vol. 27, no. 6, pp. 929-941, Jun. 2005. (Pubitemid 40889843)
8. P. Howland and H. Park, "Generalizing discriminant analysis using the generalized singular value decomposition," IEEE Trans. Pattern Anal. Mach. Intell., vol. 26, no. 8, pp. 995-1006, Aug. 2004.
9. S. Zhang and T. Sim, "Discriminant subspace analysis: A Fukunaga-Koontz approach," IEEE Trans. Pattern Anal. Mach. Intell., vol. 29, no. 10, pp. 1732-1745, Oct. 2007.
10. T. Zhang, D. Tao, and J. Yang, "Discriminative locality alignment," in Proc. 10th ECCV, 2008, pp. 725-738.
11. T. Zhang, D. Tao, X. Li, and J. Yang, "Patch alignment for dimensionality reduction," IEEE Trans. Knowl. Data Eng., vol. 21, no. 9, pp. 1299-1313, Sep. 2009.
12. H. Yu and J. Yang, "A direct LDA algorithm for high-dimensional data-With application to face recognition," Pattern Recognit., vol. 34, no. 10, pp. 2067-2070, Dec. 2001.
13. J. Yang and J. Yang, "Why can LDA be performed in PCA transformed space?" Pattern Recognit., vol. 36, no. 2, pp. 563-566, 2003. (Pubitemid 35212848)
14. H. Cevikalp, M. Neamtu, M. Wilkes, and A. Barkana, "Discriminative common vectors for face recognition," IEEE Trans. Pattern Anal. Mach. Intell., vol. 27, no. 1, pp. 4-13, Jan. 2005. (Pubitemid 40195893)
15. S. An, W. Liu, S. Venkatesh, and H. Yan, "Unified formulation of linear discriminant analysis methods and optimal parameter selection," Pattern Recognit., vol. 44, no. 2, pp. 307-319, 2011.
16. X. He, S. Yan, Y. Hu, P. Niyogi, and H. Zhang, "Face recognition using Laplacianfaces," IEEE Trans. Pattern Anal. Mach. Intell., vol. 27, no. 3, pp. 328-340, Mar. 2005. (Pubitemid 40377326)
17. X. He and P. Niyogi, "Locality preserving projections," in Advances in Neural Information Processing Systems, vol. 16. Cambridge, MA, USA: MIT Press, 2004, pp. 153-160.
18. M. Belkin and P. Niyogi, "Laplacian eigenmaps and spectral techniques for embedding and clustering," in Proc. Adv. Neural Inf. Process. Syst., vol. 1. Jan. 2002, pp. 585-592.
19. X. He, D. Cai, and W. Min, "Statistical and computational analysis of locality preserving projection," in Proc. 22nd Int. Conf. Mach. Learn., 2005, pp. 281-288. (Pubitemid 43183344)
20. H. Hotelling, "Relations between two sets of variates," Biometrika, vol. 28, nos. 3-4, pp. 321-377, 1936.
21. B. Mohar, Some Applications of Laplace Eigenvalues of Graphs. New York, NY, USA: Springer-Verlag, 1997.
22. J. Yang, D. Zhang, J. Yang, and B. Niu, "Globally maximizing, locally minimizing: Unsupervised discriminant projection with applications to face and palm biometrics," IEEE Trans. Pattern Anal. Mach. Intell., vol. 29, no. 4, pp. 650-664, Apr. 2007. (Pubitemid 46464405)
23. S. Yan, D. Xu, B. Zhang, H. Zhang, Q. Yang, and S. Lin, "Graph embedding and extensions: A general framework for dimensionality reduction," IEEE Trans. Pattern Anal. Mach. Intell., vol. 29, no. 1, pp. 40-51, Jan. 2007. (Pubitemid 46415944)
24. M. Balasubramanian and E. Schwartz, "The Isomap algorithm and topological stability," Science, vol. 295, no. 5552, p. 7, 2002.
25. R. Wang, S. Shan, X. Chen, J. Chen, and W. Gao, "Maximal linear embedding for dimensionality reduction," IEEE Trans. Pattern Anal. Mach. Intell., vol. 33, no. 9, pp. 1776-1792, Sep. 2011.
26. B. Yang and S. Chen, "Sample-dependent graph construction with application to dimensionality reduction," Neurocomputing, vol. 74, nos. 1-3, pp. 301-314, 2010.
27. H. Zhao, S. Sun, Z. Jing, and J. Yang, "Local structure based supervised feature extraction," Pattern Recognit., vol. 39, no. 8, pp. 1546-1550, 2006. (Pubitemid 44269321)
28. L. Qiao, S. Chen, and X. Tan, "Sparsity preserving projections with applications to face recognition," Pattern Recognit., vol. 43, no. 1, pp. 331-341, 2010.
29. G. Feng, D. Hu, and Z. Zhou, "A direct locality preserving projections (DLPP) algorithm for image recognition," Neural Process. Lett., vol. 27, no. 3, pp. 247-255, 2008.
30. J. Chen, B. Li, and B. Yuan, "Face recognition using direct LPP algorithm," in Proc. 9th ICSP, Oct. 2008, pp. 1457-1460.
31. R. Li, Z. Luo, and G. Han, "Pseudo-inverse locality preserving projections," in Proc. CIS, vol. 1. 2010, pp. 363-367.
32. D. Luo, C. Ding, F. Nie, and H. Huang, "Cauchy graph embedding," in Proc. 28th Int. Conf. Mach. Learn., 2011, pp. 553-560.
33. T. Zhang, B. Fang, Y. Y. Tang, Z. Shang, and B. Xu, "Generalized discriminant analysis: A matrix exponential approach," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 40, no. 1, pp. 186-197, Feb. 2010.
34. T. Havel, I. Najfeld, and J. Yang, "Matrix decompositions of twodimensional nuclear magnetic resonance spectra," Proc. Nat. Acad. Sci. United States Amer., vol. 91, no. 17, pp. 7962-7966, 1994. (Pubitemid 24253865)
35. I. Najfeld and T. Havel, "Derivatives of the matrix exponential and their computation," Adv. Appl. Math., vol. 16, no. 3, pp. 321-375, 1995.
36. G. Franklin, D. Powell, and M. Workman, Digital Control of Dynamic Systems. Reading, MA, USA: Addison-Wesley, 1997.
37. R. Sidje and W. Stewart, "A numerical study of large sparse matrix exponentials arising in Markov chains," Comput. Statist. Data Anal., vol. 29, no. 3, pp. 345-368, 1999. (Pubitemid 29432682)
38. C. Moler and C. Van Loan, "Nineteen dubious ways to compute the exponential of a matrix," SIAM Rev., vol. 20, no. 4, pp. 801-836, 1978.
39. C. Moler and C. Van Loan, "Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later," SIAM Rev., vol. 45, no. 1, pp. 3-49, 2003.
40. L. Saul and S. Roweis, "Think globally, fit locally: Unsupervised learning of low dimensional manifolds," J. Mach. Learn. Res., vol. 4, pp. 119-155, Dec. 2003.