Kernelized sorting

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn 32, Issue 10, 2010, Pages 1809-1821

  Quadrianto, Novi ^a   Smola, Alexander J ^b   Song, Le ^c   Tuytelaars, Tinne ^d  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b YAHOO RESEARCH   (United States)

^c Carnegie Mellon University   (United States)

^d UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

Hilbert Schmidt Independence Criterion.; kernels; matching; object alignment; Sorting

Indexed keywords

DATA ANALYSIS; FUNDAMENTAL OPERATIONS; HILBERT; KERNELS; MATCHING; OBJECT ALIGNMENT; OBJECT MATCHING; OPTIMAL SOLUTIONS; QUADRATIC ASSIGNMENT PROBLEMS; SIMILARITY MEASURE; SIMPLE ALGORITHM; SPECIAL STRUCTURE;

ALIGNMENT; DATA REDUCTION; OPTIMIZATION;

SORTING;

EID: 77956054665     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.2009.184     Document Type: Article

References (33)

1. N. Quadrianto, L. Song, and A. Smola, "Kernelized Sorting," Advances in Neural Information Processing Systems, D. Koller, D. Schuurmans, Y. Bengio, and L. Bottou, eds., vol.21, pp. 12891296, MIT Press, 2009.
2. S. Gold and A. Rangarajan, "A Graduated Assignment Algorithm for Graph Matching," IEEE Trans. Pattern Analysis and Machine Intelligence, vol.18, no.4, pp. 377-388, Apr. 1996.
3. T. Caetano, L. Cheng, Q.V. Le, and A.J. Smola, "Learning Graph Matching," Proc. 11th IEEE Int'l Conf. Computer Vision, pp. 1-8,2007.
4. T. Cour, P. Srinivasan, and J. Shi, "Balanced Graph Matching," Advances in Neural Information Processing Systems, B. Scholkopf, J. Platt, and T. Hofmann, eds., vol.19, pp. 313-320, MIT Press, Dec. 2006.
5. T. Jebara, "Kernelizing Sorting, Permutation, and Alignment for Minimum Volume PCA," Proc. Conf. Computational Learning Theory, pp. 609-623 2004.
6. T. Caetano, T. Caelli, D. Schuurmans, and D. Barone, "Graphical Models and Point Pattern Matching," IEEE Trans. Pattern Analysis and Machine Intelligence, vol.28, no.10, pp. 1646-1663, Oct. 2006.
7. C. Walder, B. Scholkopf, and O. Chapelle, "Implicit Surface Modelling with a Globally Regularised Basis of Compact Support," Computer Graphics Forum, vol.25, no.3, pp. 635-644, 2006.
8. F. Steinke, B. Scholkopf, and V. Blanz, "Learning Dense 3D Correspondence," Proc. 20th Ann. Conf. Neural Information Processing Systems, pp. 1313-1320, 2007.
9. A. Smola, A. Gretton, L. Song, and B. Scholkopf, "A Hilbert Space Embedding for Distributions," Algorithmic Learning Theory, E. Takimoto, ed., Springer, 2007.
10. B. Sriperumbudur, A. Gretton, K. Fukumizu, G. Lanckriet, and B. Scholkopf, "Injective Hilbert Space Embeddings of Probability Measures," Proc. 21st Ann. Conf. Learning Theory, pp. 111-122,2008.
11. N. Aronszajn, "La Theorie Generale des Noyaux Reproduisants et ses Applications," Proc. Cambridge Philosophical Soc., vol.39, pp. 133-153, 1944.
12. K. Fukumizu, F.R. Bach, and M.I. Jordan, "Dimensionality Reduction for Supervised Learning with Reproducing Kernel Hilbert Spaces," J. Machine Learning Research, vol.5, pp. 73-99, 2004.
13. G. Finke, R.E. Burkard, and F. Rendl, "Quadratic Assignment Problems," Annals of Discrete Math., vol.31, pp. 61-82, 1987.
14. M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, 1979.
15. S. Sherman, "On a Theorem of Hardy, Littlewood, Polya, and Blackwell," Proc. Nat'l Academy of Sciences, vol.37, pp. 826-831, 1951.
16. C. McDiarmid, "On the Method of Bounded Differences," Survey in Combinatorics, pp. 148-188, Cambridge Univ. Press, 1989.
17. T.P. Dinh and L.H. An, "A D.C. Optimization Algorithm for Solving the Trust-Region SubProblem," SIAM J. Optimization, vol.8, no.2, pp. 476-505, 1988.
18. A. Yuille and A. Rangarajan, "The Concave-Convex Procedure," Neural Computation, vol.15, pp. 915-936, 2003.
19. R. Jonker and A. Volgenant, "A Shortest Augmenting Path Algorithm for Dense and Sparse Linear Assignment Problems," Computing, vol.38, pp. 325-340, 1987.
20. W. Gander, G. Golub, and U. von Matt, "A Constrained Eigenvalue Problem," Linear Algebra and Its Applications, vol.114115, pp. 815-839, 1989.
21. M. Fiedler, "Algebraic Connectivity of Graphs," Czechoslovak Math. J., vol.23, no.98, pp. 298-305, 1973.
22. F. Chung-Graham, Spectral Graph Theory. AMS, 1997.
23. F. Girosi, "An Equivalence between Sparse Approximation and Support Vector Machines," A.I. Memo no. 1606, Artificial Intelligence Laboratory, Massachusetts Inst. of Technology, 1997.
24. A.J. Smola, B. Scholkopf, and K.-R. Miiller, "The Connection between Regularization Operators and Support Vector Kernels," Neural Networks, vol.11, no.5, pp. 637-649, 1998.
25. B. Scholkopf, A.J. Smola, and K.-R. Miiller, "Nonlinear Component Analysis as a Kernel Eigenvalue Problem," Neural Computation, vol.10, pp. 1299-1319, 1998.
26. K.Q. Weinberger and L.K. Saul, "An Introduction to Nonlinear Dimensionality Reduction by Maximum Variance Unfolding," Proc. Nat'l Conf. Artificial Intelligence, 2006.
27. S. Roweis and L.K. Saul, "Nonlinear Dimensionality Reduction by Locally Linear Embedding," Science, vol.290, pp. 2323-2326, Dec. 2000.
28. T. Kohonen, "Self-Organized Formation of Topologically Correct Feature Maps," Biological Cybernetics, vol.43, pp. 59-69, 1982.
29. C.M. Bishop, M. Svensen, and C.K.I. Williams, "GTM: The Generative Topographic Mapping," Neural Computation, vol.10, no.1, pp. 215-234, 1998.
30. G. Csurka, C.R. Dance, L. Fan, J. Willamowski, and C. Bray, "Visual Categorization with Bags of Keypoints," Proc. Workshop Statistical Learning in Computer Vision, pp. 1-22, 2004.
31. D.G. Lowe, "Distinctive Image Features from Scale-Invariant Keypoints," Int'l J. Computer Vision, vol.60, pp. 91-110, 2004.
32. P. Koehn, "Europarl: A Parallel Corpus for Statistical Machine Translation," Proc. Machine Translation Summit X, pp. 79-86, 2005.
33. W.A. Gale and K.W. Church, "A Program for Aligning Sentences in Bilingual Corpora," Proc. Meeting of the Assoc. for Computational Linguistics, pp. 177-184, 1991.