Log-euclidean metric learning on symmetric positive definite manifold with application to image set classification

32nd International Conference on Machine Learning, ICML 2015

Volumn 1, Issue , 2015, Pages 720-729

  Huangt, Zhiwu ^a,b   Wang, Ruiping ^a,c   Shan, Shiguang ^a,c   Li, Xianqiu ^a,b   Chen, Xilin ^a,c  

^a INSTITUTE OF COMPUTING TECHNOLOGY   (China)

^b UNIVERSITY OF CHINESE ACADEMY OF SCIENCES   (China)

^c Cooperative Medianet Innovation Center ^*  (China)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; LEARNING SYSTEMS; OPTIMIZATION;

CLASSIFICATION TASKS; DATA REPRESENTATIONS; DISCRIMINABILITY; GEOMETRICAL STRUCTURE; MATRIX LOGARITHM; METRIC LEARNING; OPTIMIZATION PROBLEMS; SYMMETRIC POSITIVE DEFINITE;

IMAGE CLASSIFICATION;

EID: 84969523506     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (50)

1. Absil, P-A, Mahony, R., and Sepulchre, R. Optimization algorithms on matrix manifolds. Princeton University Press, 2008.
2. Araari, S. and Nagaoka, H. Methods of information geometry. Oxford University Press, 2000.
3. Arandjelovic, O., Shakhnarovich, G., Fisher, J.W., Cipol-la, R., and Darrell, T. Face recognition with image sets using manifold density divergence. In CVPR, 2005.
4. Arsigny, V., Fillard, P., Pennec, X., and Ayache., N. Fast and simple computations on tensors with Log-Euclidean metrics. Res. Rep. RR-5584JNRIA, 2005.
5. Arsigny, V., Fillard, P., Pennec, X., and Ayache, N. Log-Euclidean metrics for fast and simple calculus on diffusion tensors. Magnetic resonance in medicine, 2006.
6. Arsigny, V., Fillard, P., Pennec, X., and Ayache, N. Geometric means in a novel vector space structure on symmetric positive-definite matrices. SIAM J. Matrix Analysis and Applications, 29(l):328-347, 2007.
7. Bregman, L.M. The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming. USSR computational mathematics and mathematical physics, 7(3): 200-217, 1967.
8. Carreira, J., Caseiro, R., Caseiro, J., and Sminchisescu, C. Semantic segmentation with second-order pooling. In ECCV, 2012.
9. Censor, Y. and Zenios, S. Parallel optimization: Theory, algorithms, and applications. Oxford University Press, 1997.
10. Cevikalp, H. and Triggs, B. Face recognition based on image sets. In CVPR, 2010.
11. Davis, J. V, Kulis, B., Jain, P., Sra, S., and Dhillon, I. S. Information-theoretic metric learning. In ICML, 2007.
12. Golub, G.H., Van, L., and Charles, F. Matrix computations, volume 3. Johns Hopkins University Press, 2012.
13. Hamm, J. and Lee, D. D. Grassmann discriminant analysis: a unifying view on subspace-based learning. In ICML, 2008.
14. Harandi, M. T, Sanderson, C, Shirazi, S., and Lovell, B. C. Graph embedding discriminant analysis on Grassman-nian manifolds for improved image set matching. In CVPR, 2011.
15. Harandi, M. T, Sanderson, C, Hartley, R., and Lovell, B. C. Sparse coding and dictionary learning for symmetric positive definite matrices: A kernel approach. In ECCV. 2012.
16. Harandi, M.T., Salzmann, M., and Hartley, R. From manifold to manifold: Geometry-aware dimensionality reduction for SPD matrices. In ECCV. 2014.
17. Hayat, M., Bennamoun, M., and An, S. Reverse training: An efficient approach for image set classification. In ECCV, 2014.
18. Hu, Y., Mian, A.S., and Owens, R. Sparse approximated nearest points for image set classification. In CVPR, 2011.
19. Huang, Z., Wang, R., Shan, S., and Chen, X. Learning Euclidean-to-Riemannian metric for point-to-set classification. In CVPR, 2014.
20. Huang, Z., Shan, S., Wang, R., Zhang, H., Lao, S., Kuer-ban, A., and Chen, X. A benchmark and comparative study of video-based face recognition on COX face database. IEEE T-IP, 2015a.
21. Huang, Z., Wang, R., Shan, S., and Chen, X. Face recognition on large-scale video in the wild with hybrid Euclidean-and-Riemannian metric learning. Pattern Recognition, 2015b.
22. Huang, Z,, Wang, R., Shan, S., and Chen, X. Projection metric learning on Grassmann manifold with application to video based face recognition. In CVPR, 2015c.
23. Jayasumana, S., Hartley, R., Salzmann, M., Li, H., and Harandi, M.T. Kernel methods on the Riemannian manifold of symmetric positive definite matrices. In CVPR, 2013.
24. Jung, S., Dryden, I.L., and Marron, J.S. Analysis of principal nested spheres. Biometrika, 99(3):551-568, 2012.
25. Kim, M., Kumar, S., Pavlovic, V., and Rowley, H. Face tracking and recognition with visual constraints in real-world videos. In CVPR, 2008.
26. Kim, T. K., Kittler, J., and Cipolla, R. Discriminative learning and recognition of image set classes using canonical correlations. IEEE T-PAMI, 29(6): 1005-1018,2007.
27. Kulis, B., Sustik, M.A., and Dhillon, I. S. Low-rank kernel learning with bregman matrix divergences. JMLR, 10: 341-376, 2009.
28. Leibe, B. and Schiele, B. Analyzing appearance and contour based methods for object categorization. In CVPR, 2003.
29. Li, P., Wang, Q., Zuo, W., and Zhang, L. Log-Euclidean kernels for sparse representation and dictionary learning. In ICCV, 2013.
30. Lovric, M., Min-Oo, M., and Ruh, E.A. Multivariate normal distributions parametrized as a Riemannian symmetric space. Journal of Multivariate Analysis, 74(l):36-48, 2000.
31. Lu, J., Wang, G., and Moulin, P. Image set classification using holistic multiple order statistics features and localized multi-kernel metric learning. In ICCV, 2013.
32. Lu, J., Wang, G., Deng, W, and Moulin, P. Simultaneous feature and dictionary learning for image set based face recognition. In ECCV, 2014.
33. Mahmood, A., Mian, A., and Owens, R. Semi-supervised spectral clustering for image set classification. In CVPR, 2014.
34. Minh, H.Q., Biagio, M.S., and Murino, V. Log-hilbert-schmidt metric between positive definite operators on Hilbert spaces. In NIPS, 2014.
35. Pennec, X., Fillard, P., and Ayache, N. A Riemannian framework for tensor computing. IJCV, 66(1):41-66, 2006.
36. Shakhnarovich, G., Fisher, J.W., and Darrell, T. Face recognition from long-term observations. In ECCV, 2002.
37. Sherman, J. and Morrison, W. J. Adjustment of an inverse matrix corresponding to a change in one element of a given matrix. The Annals of Mathematical Statistics, pp. 124-127, 1950.
38. Sivalingam, R., Morellas, V., Boley, D., and Pa-panikolopoulos, N. Metric learning for semi-supervised clustering of region covariance descriptors. In ICDSC, 2009.
39. Sra, S. A new metric on the manifold of kernel matrices with application to matrix geometric means. In NIPS, 2012.
40. Tosato, D., Farenzena, M., Cristani, M., Spera, M., and Murino, V. Multi-class classification on Riemannian manifolds for video surveillance. In ECCV, 2010.
41. Vemulapalli, R. and Jacobs, D. W. Riemannian metric learning for symmetric positive definite matrices. In arX-iv, 2015.
42. Vemulapalli, R" Pillai, J.K., and Chellappa, R. Kernel learning for extrinsic classification of manifold features. In CVPR, 2013.
43. Wang, R. and Chen, X. Manifold discriminant analysis. In CVPR, 2009.
44. Wang, R., Shan, S., Chen, X., and Gao, W. Manifold-Manifold distance with application to face recognition based on image set. In CVPR, 2008.
45. Wang, R., Guo, H., Davis, L., and Dai, Q. Covariance discriminative learning: A natural and efficient approach to image set classification. In CVPR, 2012.
46. Wang, W., Wang, R., Huang, Z., Shan, S., and Chen, X. Discriminant analysis on Riemannian manifold of Gaussian distributions for face recognition with image sets. In CVPR, 2015.
47. Wolf, L., Hassner, T., and Maoz, I. Face recognition in unconstrained videos with matched background similarity. In CVPR, 2011.
48. Yang, J., Zhang, D., Frangi, A.F., and Yang, J. Two-dimensional PCA: a new approach to appearance-based face representation and recognition. IEEE T-PAMI, 26 (1):131-137, 2004.
49. Yang, M., Zhu, P., VanGool, L., and Zhang, L. Face recognition based on regularized nearest points between image sets. In FG, 2013.
50. Zhu, P., Zhang, L., Zuo, W., and Zhang, D. From point to set: Extend the learning of distance metrics. In ICCV, 2013.