Subspaces versus submanifolds: A comparative study in small sample size problem

International Journal of Pattern Recognition and Artificial Intelligence

Volumn 23, Issue 3, 2009, Pages 463-490

  Huang, Hong ^a   Li, Jianwei ^a,b   Feng, Hailiang ^a  

^a CHONGQING UNIVERSITY   (China)

^b CHONGQING UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Face recognition; Kernel machines; Out of example; Submanifold; Subspace; Supervised learning

Indexed keywords

AUTOMATIC FACE RECOGNITION; CLASSIFICATION ACCURACY; COMPARATIVE STUDIES; EIGENFACES; FACE DATABASE; FACE IMAGES; FISHER-FACES; IMAGE SPACE; ISOMETRIC FEATURE MAPPING; KERNEL MACHINES; LOCALLY LINEAR EMBEDDING; MANIFOLD LEARNING; NUMBER OF SAMPLES; OUT-OF-EXAMPLE; SAMPLE SPACE; SMALL SAMPLE SIZE PROBLEMS; SUB-SPACE METHODS; SUBMANIFOLD; SUBMANIFOLDS; SUBSPACE; THEORETICAL ASPECTS; TRAINING SETS;

BIOMETRICS; SUPERVISED LEARNING;

FACE RECOGNITION;

EID: 67650703137     PISSN: 02180014     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218001409007168     Document Type: Article

References (53)

1. B. Batagelj and F. Solina, Face recognition in different subspaces - a comparative study, Proc. ICEIS'06, Paphos, Cyprus (2006), pp. 71-80.
2. A. U. Batur and M. H. Hayes, Linear subspace for illumination robust face recognition, Proc. IEEE Int. Conf. Computer Vision and Pattern Recognition (2001), pp. 296-301.
3. P. N. Belhumeur and J. P. Hespanha, Eigenfaces vs. fisherfaces: recognition using class specific linear projection, IEEE Trans. Patt. Anal. Mach. Intell. 19(7) (1997) 711-720.
4. M. Belkin and P. Niyogi, Laplacian eigenmaps and spectral techniques for embedding and clustering, Advances in Neural Information Processing Systems (NIPS) (2001), pp. 585-591.
5. Y. Bengio, O. Delalleau and N. Le Roux, Learning eigenfunctions links spectral embedding and Kernel PCA, Neural Comput. 16(10) (2004) 2197-2219.
6. Y. Bengio, J. F. Paiement, P. Vincent et al., Out-of-sample extensions for LLE, Isomap, MDS, eigenmaps, and spectral clustering, Adv. Neural Inform. Process. Syst. 16 (2004) 177-184.
7. M. Brand, From subspaces to submanifolds, Proc. 15th British Machine Vision Conference, British Machine Vision Association, London, UK (2004).
8. H. J. Chen and W. Wei, Geodesic Gabriel graph based supervised nonlinear manifold learning, Intell. Comput. Sign. Process. Patt. Recogn. 345 (2006) 882-888.
9. H. Choi, S. Choi and R. K. Isomap, Patt. Recogn. 40(3) (2007) 853-862.
10. T. F. Cox and M. A. A. Cox, Multidimensional Scaling, 2nd edn. (Chapman and Hall/CRC, 2001).
11. L. D. David and G. Carrie, When does isomap recover the natural parametrization of families of articulated images? Technical Report, Department of Statistics, Stanford University (2002).
12. M. P. Dickens, W. A. Smith, W. Jing, et al., Face recognition using principal geodesic analysis and manifold, learning, Proc. 3th Iberian Conf. Pattern Recognition and Image Analysis (2007), pp. 426-434.
13. D. L. Donoho and C. Grimes, Hessian eigenmaps: new locally linear embedding techniques for high-dimensional data, Proc. Nat. Acad. Sci. 102(21) (2005) 7426-7431.
14. X. Geng, D. C. Zhan and Z. H. Zhou, Supervised nonlinear dimensionality reduction for visualization and classification, IEEE Trans. Syst Man Cybern. Part B-Cybern. 35 (2005) 1098-1107.
15. D. Guang and Y. Dit-Yan, Tensor embedding methods, Proc. 21th National Conf. Artificial Intelligence (AAAI-2006), pp. 330-335.
16. X. He, C. Deng, S. Yan et al., Neighborhood preserving embedding, Proc. 10th IEEE Int. Conf. Computer Vision (ICCV'05) (2005), pp. 1208-1213.
17. X. He and P. Niyogi, Locality preserving projections, Adv. Neural Inform. Process. Syst. 16 (2004) 37.
18. X. He, S. Yan, Y. Hu et al., Face recognition using laplacianfaces, IEEE Trans. Patt. Anal. Mach. Intell. 27(3) (2005) 328-340.
19. P. Howland, J. L. Wang and H. Park, Solving the small sample size problem in face recognition using generalized discriminant analysis, Patt. Recogn. 39 (2006) 277-287.
20. C. Hwann-Tzong, C. Huang-Wei and L. Tyng-Luh, Local discriminant embedding and its variants, Proc. IEEE Computer Society Conf. Computer Vision and Pattern Recognition 2 (2005) 846-853.
21. O. Kouropteva, O. Okun, A. Hadid et al., Beyond locally linear embedding algorithm, Technical Report MVG-01-2002, University of Oulu (2002).
22. S. Lafon and A. B. Lee, Diffusion maps and coarse-graining: a unified framework for dimensionality reduction, graph partitioning, and dataset parameterization, IEEE Trans. Patt. Anal. Mach. Intell. 28(9) (2006) 1393-1403.
23. S. Z. Li and A. K. Jain, (eds.), Handbook of Face Recognition (Springer-Verlag, 2004).
24. X. L. Li, S. Lin, S. C. Yan et al., Discriminant locally linear embedding with high-order tensor data, IEEE Trans. Syst. Man Cybern. Part B-Cybern. 38 (2007) 342-352.
25. H. Li, L. Teng, W. Chen et al., Supervised learning on local tangent space, in Lecture Notes on Computer Science, Vol. 3496 (Springer Verlag, Berlin, Germany, 2005), pp. 546-551.
26. X. M. Liu, J. W. Yin, Z. L. Feng et al., Orthogonal neighborhood preserving embedding for face recognition, IEEE Int. Conf. Image Processing (2007), pp. 133-136.
27. K. Lu and X. F. He, Image retrieval based on incremental subspace learning, Patt. Recogn. 38(11) (2005) 2047-2054.
28. A. M. Martinez and A. C. Kak, PCA versus LDA, IEEE Trans. Patt. Anal. Mach. Intell. 23(2) (2001) 228-233.
29. N. Mekuz, C. Bauckhage and J. K. Tsotsos, Face recognition with weighted locally linear embedding, Proc. 2th Canadian Conf. Computer and Robot Vision (2005), pp. 290-296.
30. P. Navarrete and J. Ruiz-del-Solar, Analysis and comparison of eigenspace-based face recognition approaches, Int. J. Patt. Recogn. Artif. Intell. 16(2) (2002) 817-830.
31. P. Navarrete and J. Ruiz-del-Solar, Kernel-based face recognition by a reformulation of kernel machines, Adv. Soft Comput.-Engin. Des. Manuf., Springer Engineering Series (2003), pp. 183-196.
32. P. J. Phillips, H. Moon, S. Rizvi et al., The FERET evaluation methodology for face-recognition algorithms, IEEE Trans. Patt. Anal. Mach. Intell. 22(10) (2000) 1090-1104.
33. S. T. Roweis and L. K. Saul, Nonlinear dimensionality reduction by locally linear embedding, Science 290(5500) (2000) 2323-2326.
34. J. Ruiz-del-Solar and P. Navarrete, Eigenspace-based face recognition: a comparative study of different approaches, IEEE Trans. Syst. Man Cybern.: Part C 35(3) (2005) 315-325.
35. V. Saltenis, Constrained optimization of the stress function for multidimensional scaling, Lecture Notes on Computer Science, Vol. 3991 (Springer Verlag, Berlin, Germany, 2005), pp. 704-711.
36. L. Saul and S. Roweis, Think globally, fit locally: unsupervised learning of nonlinear manifolds, J. Mach. Learn. Res. 4 (2003) 119-155.
37. T. Sim, S. Baker and M. Bsat, The CMU database, IEEE Trans. Patt. Anal. Mach. Intell. 25 (2003) 1615-1618.
38. Y. W. Teh and S. T. Roweis, Automatic alignment of hidden, representations, Adv. Neural Inform. Process. Syst. 15 (2002) 841-848.
39. J. B. Tenenbaum, Mapping a manifold of perceptual observations, in Advances in Neural Information Processing Systems (Cambridge, MIT Press, 1998).
40. J. B. Tenenbaum, V. de Silva and J. C. Langford, A global geometric framework for nonlinear dimensionality reduction, Science 290(5500) (2000) 2319-2323.
41. M. Turk and A. Pentland, Eigenfaces for recognition, J. Cogn. Neurosci. 3(1) (1991) 71-86.
42. H. X. Wand, W. M. Zheng, Z. L. Hu et al., Local and weighted maximum margin discriminant analysis, IEEE Conf. Computer Vision and Pattern Recognition (CVPR'07) (2007), pp. 532-539.
43. H. H. Wang, Y. Zhou, X. L. Ge et al., Subspace evolution analysis for face representation and recognition, Patt. Recogn. 40 (2007) 335-338.
44. L. Wiskott, J. M. Fellous, N. Kruger, et al., Face recognition by elastic bunch graph matching, IEEE Trans. Patt. Anal. Mach. Intell. 19(7) (1997) 775-779.
45. Y. M. Wu, K. L. Chan and L. Wang, Face recognition based on discriminative manifold learning, Proc. 17th Int. Conf. Pattern Recognition, Vol. 4, pp. 171-174.
46. D. Xu, S. C. Yan, D. C. Tao et al., Marginal Fisher analysis and its variants for human gait recognition and content-based image retrieval, IEEE Trans. Imag. Process. 16 (2007) 2811-2821.
47. M. H. Yang, Extended isomap for pattern classification, Proc. 18th Nat. Conf. Artificial Intelligence (AAAI 2002), pp. 224-229.
48. J. Yang, D. Zhang, J. Y. Yang et al., Globally maximizing, locally minimizing: unsupervised discriminant projection with applications to face and palm biometrics, IEEE Trans. Patt. Anal. Mach. Intell. 29 (2007) 650-664.
49. F. Zhang, Nonlinear feature extraction and dimension reduction by polygonal principal curves, Int. J. Patt. Recogn. Artif. Intell. 20(1) (2006) 63-78.
50. J. P. Zhang, S. Z. Li and J. Wang, Nearest manifold approach for face recognition, Proc. 6th IEEE Int. Conf. Automatic Face and Gesture Recognition (2004), pp. 223-228.
51. Z. Zhang and H. Zha, Principal manifolds and nonlinear dimensionality reduction via local tangent space alignment, SIAM J. Sci. Comput. 26(1) (2004) 313-338.
52. W. Zhao, R. Chellappa, P. J. Phillips and A. Rosenfeld, Face recognition: a literature survey, ACM Comput. Surv. 35(4) (2003) 399-458.
53. D. L. Zhao, Z. C. Lin and X. O. Tang, Laplacian PCA and its applications, 11th IEEE Int. Conf. Computer Vision (2007), pp. 2012-2019.