Grassmann discriminant analysis: A unifying view on subspace-based learning

Proceedings of the 25th International Conference on Machine Learning

Volumn , Issue , 2008, Pages 376-383

  Hamm, Jihun ^a   Lee, Daniel D ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DISCRIMINANT ANALYSIS; EDUCATION; FEATURE EXTRACTION; LEARNING SYSTEMS; PROBLEM SOLVING; ROBOT LEARNING;

BASIC ELEMENTS; CAUCHY KERNELS; EUCLIDEAN DISTANCES; EUCLIDEAN SPACES; FEATURE EXTRACTION AND CLASSIFICATIONS; GRASSMANN MANIFOLDS; KERNEL FUNCTIONS; LEARNING FRAMEWORKS; LEARNING METHODS; LINEAR SUBSPACES; REAL IMAGES; SUB SPACES; STATE-OF-THE-ART ALGORITHMS;

LEARNING ALGORITHMS;

EID: 56449127949     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (27)

1. Absil, P., Mahony, R., & Sepulchre, R. (2004). Riemannian geometry of Grassmann manifolds with a view on algorithmic computation. Acta Appl. Math., 80, 199-220.
2. Chang, J.-M., Beveridge, J. R., Draper, B. A., Kirby, M., Kley, H., & Peterson, C. (2006). Illumination face spaces are idiosyncratic. IPCV (pp. 390-396).
3. Chikuse, Y. (2003). Statistics on special manifolds, lecture notes in statistics, vol. 174. New York: Springer.
4. Edelman, A., Arias, T. A., & Smith, S. T. (1999). The geometry of algorithms with orthogonality constraints. SIAM J. Matrix Anal. Appl., 20, 303-353.
5. Farago, A., Linder, T., & Lugosi, G. (1993). Fast nearest-neighbor search in dissimilarity spaces. IEEE Trans. Pattern Anal. Mach. Intell., 15, 957-962.
6. Fukui, K., & Yamaguchi, O. (2003). Face recognition using multi-viewpoint patterns for robot vision. Int. Symp. of Robotics Res. (pp. 192-201).
7. Fukunaga, K. (1990). Introduction to statistical pattern recognition (2nd ed.). San Diego, CA, USA: Academic Press Professional, Inc.
8. Georghiades, A. S., Belhumeur, P. N., & Kriegman, D. J. (2001). From few to many: Illumination cone models for face recognition under variable lighting and pose. IEEE Trans. Pattern Anal. Mach. Intell., 23, 643-660.
9. Golub, G. H., & Loan, C. F. V. (1996). Matrix computations (3rd ed.). Baltimore, MD, USA: Johns Hopkins University Press.
10. Haasdonk, B. (2005). Feature space interpretation of svms with indefinite kernels. IEEE Trans. Pattern. Anal. Mach. Intell., 27, 482-492.
11. Hein, M., Bousquet, O., & Schölkopf, B. (2005). Maximal margin classification for metric spaces. J. Comput. Syst. Sci., 71, 333-359.
12. Kim, T.-K., Kittler, J., & Cipolla, R. (2007). Discriminative learning and recognition of image set classes using canonical correlations. IEEE Trans. Pattern Anal. Mach. Intell., 29, 1005-1018.
13. Kondor, R. I., & Jebara, T. (2003). A kernel between sets of vectors. Proc. of the 20th Int. Conf. on Mach. Learn. (pp. 361-368).
14. Leibe, B., & Schiele, B. (2003). Analyzing appearance and contour based methods for object categorization. CVPR, 02, 409.
15. Ong, C. S., Mary, X., Canu, S., & Smola, A. J. (2004). Learning with non-positive kernels. Proc. of 21st Int. Conf. on Mach. Learn. (p. 81). New York, NY, USA: ACM.
16. Pekalska, E., Paclik, P., & Duin, R. P. W. (2002). A generalized kernel approach to dissimilarity-based classification. J. Mach. Learn. Res., 2, 175-211.
17. Sakano, H.; Mukawa, N. (2000). Kernel mutual subspace method for robust facial image recognition. Proc. of Int. Conf. on Knowledge-Based Intell. Eng. Sys. and App. Tech. (pp. 245-248).
18. Schoenberg, I. J. (1938). Metric spaces and positive definite functions. Trans. Amer. Math. Soc., 44, 522-536.
19. Schölkopf, B., & Smola, A. J. (2001). Learning with kernels: Support vector machines, regularization, optimization, and beyond. Cambridge, MA, USA: MIT Press.
20. Shakhnarovich, G., John W. Fisher, I., & Darrell, T. (2002). Face recognition from long-term observations. Proc. of the 7th Euro. Conf. on Computer Vision (pp. 851-868). London, UK.
21. Turk, M., & Pentland, A. P. (1991). Eigenfaces for recognition. J. Cog. Neurosc., 3, 71-86.
22. Vishwanathan, S., & Smola, A. J. (2004). Binet-cauchy kernels. Proc. of Neural Info. Proc. Sys..
23. Wang, L., Wang, X., & Feng, J. (2006). Subspace distance analysis with application to adaptive bayesian algorithm for face recognition. Pattern Recogn., 39, 456-464.
24. Wolf, L., & Shashua, A. (2003). Learning over sets using kernel principal angles. J. Mach. Learn. Res., 4, 913-931.
25. Wong, Y.-C. (1967). Differential geometry of Grassmann manifolds. Proc. of the Nat. Acad. of Sci., Vol. 57, 589-594.
26. Yamaguchi, O., Fukui, K., & Maeda, K. (1998). Face recognition using temporal image sequence. Proc. of the 3rd. Int. Conf. on Face & Gesture Recognition (p. 318). Washington, DC, USA: IEEE Computer Society.
27. Zhou, S. K., & Chellappa, R. (2006). From sample similarity to ensemble similarity: Probabilistic distance measures in reproducing kernel hilbert space. IEEE Trans. Pattern Anal. Mach. Intell., 28, 917-929.