Optimizing over radial kernels on compact manifolds

Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition

Volumn , Issue , 2014, Pages 3802-3809

  Jayasumana, Sadeep ^a   Hartley, Richard ^a   Salzmann, Mathieu ^a   Li, Hongdong ^b   Harandi, Mehrtash ^b  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b CSIRO   (Australia)

Author keywords

Grassmann; kernel methods; kernels on manifolds; MKL; Riemannian manifolds; shape analysis

Indexed keywords

LEARNING ALGORITHMS; SUPPORT VECTOR MACHINES;

GRASSMANN; GRASSMANN MANIFOLD; KERNEL METHODS; POSITIVE DEFINITE; POSITIVE DEFINITE KERNELS; RIEMANNIAN MANIFOLD; SHAPE ANALYSIS; SHAPE RECOGNITION;

COMPUTER VISION;

EID: 84911417340     PISSN: 10636919     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CVPR.2014.480     Document Type: Conference Paper

References (26)

1. A. Argyriou, R. Hauser, C. A. Micchelli, and M. Pontil. A DC-Programming Algorithm for Kernel Selection. In ICML, 2006.
2. N. Ayat, M. Cheriet, and C. Suen. Automatic Model Selection for the Optimization of SVM Kernels. Pattern Recognition, 2005.
3. C. Berg, J. P. R. Christensen, and P. Ressel. Harmonic Analysis on Semigroups. Springer, 1984.
4. O. Chapelle, V. Vapnik, O. Bousquet, and S. Mukherjee. Choosing Multiple Parameters for Support Vector Machines. In Machine Learning, 2002.
5. M. Eitz, J. Hays, and M. Alexa. How Do Humans Sketch Objects? ACM Trans. Graph. (Proc. SIGGRAPH), 2012.
6. K. Fukumizu, B. K. Sriperumbudur, A. Gretton, and B. Schlkopf. Characteristic Kernels on Groups and Semigroups. In NIPS, 2008.
7. M. Gönen and E. Alpaydin. Multiple Kernel Learning Algorithms. JMLR, 2011.
8. J. Hamm and D. D. Lee. Grassmann Discriminant Analysis: a Unifying View on Subspace-Based Learning. In ICML, 2008.
9. M. T. Harandi, C. Sanderson, S. Shirazi, and B. C. Lovell. Graph Embedding Discriminant Analysis on Grassmannian Manifolds for Improved Image Set Matching. In CVPR, 2011.
10. S. Jayasumana, R. Hartley, M. Salzmann, H. Li, and M. Ha-randi. Kernel Methods on the Riemannian Manifold of Symmetric Positive Definite Matrices. In CVPR, 2013.
11. S. Jayasumana, M. Salzmann, H. Li, and M. Harandi. A Framework for Shape Analysis via Hilbert Space Embedding. In ICCV, 2013.
12. D. G. Kendall. Shape Manifolds, Procrustean Metrics, and Complex Projective Spaces. Bulletin of the London Mathematical Society, 1984.
13. M. Kim, S. Kumar, V. Pavlovic, and H. A. Rowley. Face Tracking and Recognition with Visual Constraints in Real-World Videos. In CVPR, 2008.
14. G. R. G. Lanckriet, N. Cristianini, P. Bartlett, L. E. Ghaoui, and M. I. Jordan. Learning the Kernel Matrix with Semidef-inite Programming. JMLR, 2004.
15. O. M. Parkhi, A. Vedaldi, A. Zisserman, and C. V. Jawahar. Cats and Dogs. In CVPR, 2012.
16. A. Rakotomamonjy, U. D. Rouen, F. Bach, S. Canu, and Y. Grandvalet. SimpleMKL. JMLR, 2008.
17. I. J. Schoenberg. Positive Definite Functions on Spheres. Duke Mathematical Journal, 1942.
18. B. Schölkopf and A. J. Smola. Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. MIT Press, 2002.
19. S. K. G. Shirazi, R. Safabakhsh, and M. Shamsi. Learning Translation Invariant Kernels for Classification. JMLR, 2010.
20. B. K. Sriperumbudur, K. Fukumizu, and G. R. G. Lanckriet. Universality, Characteristic Kernels and RKHS Embedding of Measures. JMLR, 2011.
21. A. Srivastava, I. Jermyn, and S. Joshi. Riemannian Analysis of Probability Density Functions with Applications in Vision. In CVPR, 2007.
22. I. Steinwart. On the Influence of the Kernel on the Consistency of Support Vector Machines. JMLR, 2001.
23. R. Vemulapalli, J. K. Pillai, and R. Chellappa. Kernel Learning for Extrinsic Classification of Manifold Features. In CVPR, 2013.
24. J. Wang, K. Markert, and M. Everingham. Learning Models for Object Recognition from Natural Language Descriptions. In BMVC, 2009.
25. Y. Wang and G. Mori. Human Action Recognition by Semilatent Topic Models. PAMI, 2009.
26. K. Q. Weinberger, F. Sha, and L. K. Saul. Learning a Kernel Matrix for Nonlinear Dimensionality Reduction. In ICML, 2004.