Stochastic Dykstra algorithms for metric learning with positive definite covariance descriptors

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 9910 LNCS, Issue , 2016, Pages 786-799

  Matsuzawa, Tomoki ^a   Relator, Raissa ^b   Sese, Jun ^b   Kato, Tsuyoshi ^a  

^a GUNMA UNIVERSITY   (Japan)

^b NATIONAL INSTITUTE OF ADVANCED INDUSTRIAL SCIENCE AND TECHNOLOGY AIST   (Japan)

Author keywords

Convex optimization; Covariance descriptor; Dykstra algorithm; Metric learning; Stochastic optimization

Indexed keywords

CONVEX OPTIMIZATION; GEOMETRY; ITERATIVE METHODS; PATTERN RECOGNITION;

COVARIANCE DESCRIPTOR; DESCRIPTORS; HALF SPACES; METRIC LEARNING; OPTIMAL SOLUTIONS; POSITIVE DEFINITE; STOCHASTIC OPTIMIZATIONS;

LEARNING ALGORITHMS;

EID: 84990050292     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-319-46466-4_47     Document Type: Conference Paper

References (23)

1. Jayasumana, S., Hartley, R., Salzmann, M., Li, H., Harandi, M.T.: Kernel methods on the Riemannian manifold of symmetric positive definite matrices. In: CVPR, pp. 73-80. IEEE (2013)
2. Huang, Z., Wang, R., Shan, S., Li, X., Chen, X.: Log-euclidean metric learning on symmetric positive definite manifold with application to image set classification. In: ICML, pp. 720-729 (2015)
3. Vemulapalli, R., Jacobs, D.W.: Riemannian metric learning for symmetric positive definite matrices. arXiv:1501.02393 (2015)
4. Yger, F., Sugiyama, M.: Supervised logeuclidean metric learning for symmetric positive definite matrices. arXiv:1502.03505 (2015)
5. Pennec, X., Fillard, P., Ayache, N.: A Riemannian framework for tensor computing. Int. J. Comput. Vis. 66(1), 41-66 (2006)
6. Sra, S.: A new metric on the manifold of kernel matrices with application to matrix geometric means. In: Advances in Neural Information Processing Systems, pp. 144-152 (2012)
7. Wang, Z., Vemuri, B.C.: An affine invariant tensor dissimilarity measure andits applications to tensor-valued image segmentation. In: Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 1, pp. I-228. IEEE (2004)
8. Arsigny, V., Fillard, P., Pennec, X., Ayache, N.: Log-Euclidean metrics for fast and simple calculus on diffusion tensors. Magnetic Resonance Med. 56(2), 411-421 (2006)
9. Dryden, I.L., Koloydenko, A., Zhou, D.: Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging. Ann. Appl. Stat. 1102-1123 (2009)
10. Davis, J.V., Kulis, B., Jain, P., Sra, S., Dhillon, I.S.: Information-theoretic metric learning. In: ICML, pp. 209-216. ACM (2007)
11. Kato, T., Nagano, N.: Metric learning for enzyme active-site search. Bioinformatics 26(21), 2698-2704 (2010)
12. Relator, R., Nagano, N., Kato, T.: Using Bregman divergence regularized machine for comparison of molecular local structures. IEICE Trans. Inf. Syst. 1, E99-D (2016)
13. Censor, Y., Reich, S.: The Dykstra algorithm with Bregman projections. Comm. Appl. Anal. 2, 407-419 (1998)
14. Dykstra, R.L.: An algorithm for restricted least squares regression. J. Am. Stat. Assoc. 78(384), 837-842 (1983)
15. Sivalingam, R., Morellas, V., Boley, D., Papanikolopoulos, N.: Metric learning for semi-supervised clustering of region covariance descriptors. In: Third ACM/IEEE International Conference on Distributed Smart Cameras, (ICDSC 2009) (2009)
16. Tosato, D., Farenzena, M., Spera, M., Murino, V., Cristani, M.: Multi-class classification on riemannian manifolds for video surveillance. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010. LNCS, vol. 6312, pp. 378-391. Springer, Heidelberg (2010). doi:10.1007/978-3-642-15552-9_28
17. Horev, I., Yger, F., Sugiyama, M.: Geometry-aware principal component analysis for symmetric positive definite matrices. In: Proceedings of the Fourth Asian Conference on Machine Learning (ACML2015), vol. 45. JMLR Workshop and Conference Proceedings, Hong Kong, China, pp. 1-16, 20-22 November 2015
18. Cristianini, N., Shawe-Taylor, J., Elisseeff, A., Kandola, J.S.: On kernel-target alignment. In: Dietterich, T.G., Becker, S., Ghahramani, Z., (eds.) NIPS, pp. 367-373. MIT Press (2001)
19. Bottou, L.: Large-scale machine learning with stochastic gradient descent. In: Lechevallier, Y., Saporta, G., (eds.) COMPSTAT 2010, pp. 177-187. Springer, Heidelberg (2010)
20. Johnson, R., Zhang, T.: Accelerating stochastic gradient descent using predictive variance reduction. In: Advances in Neural Information Processing Systems 26, Proceedings of a meeting held 5-8 December 2013, Lake Tahoe, Nevada, United States, pp. 315-323 (2013)
21. Roux, N.L., Schmidt, M., Bach, F.R.: A stochastic gradient method with an exponential convergence rate for finite training sets. In Pereira, F., Burges, C., Bottou, L.,Weinberger, K., (eds.) Advances in Neural Information Processing Systems, vol. 25, pp. 2663-2671. Curran Associates, Inc. (2012)
22. Shalev-Shwartz, S., Singer, Y., Srebro, N., Cotter, A.: Pegasos: primal estimated sub-gradient solver for SVM. Math. Program. 127(1), 3-30 (2011)
23. Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, New York (2004)