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Issue No.10 - October (2010 vol.32)
pp: 1809-1821
Alex J. Smola , Yahoo! Research, Santa Clara
Le Song , Carnegie Mellon University, Pittsburgh
Novi Quadrianto , Australian National University and NICTA, Canberra
Object matching is a fundamental operation in data analysis. It typically requires the definition of a similarity measure between the classes of objects to be matched. Instead, we develop an approach which is able to perform matching by requiring a similarity measure only within each of the classes. This is achieved by maximizing the dependency between matched pairs of observations by means of the Hilbert-Schmidt Independence Criterion. This problem can be cast as one of maximizing a quadratic assignment problem with special structure and we present a simple algorithm for finding a locally optimal solution.
Sorting, matching, kernels, object alignment, Hilbert-Schmidt Independence Criterion.
Alex J. Smola, Le Song, Novi Quadrianto, "Kernelized Sorting", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.32, no. 10, pp. 1809-1821, October 2010, doi:10.1109/TPAMI.2009.184
[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. 1289-1296, 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. Schölkopf, 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. Schölkopf, 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. Schölkopf, 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. Schölkopf, "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. Schölkopf, "Injective Hilbert Space Embeddings of Probability Measures," Proc. 21st Ann. Conf. Learning Theory, pp. 111-122, 2008.
[11] N. Aronszajn, "La Théorie Générale des Noyaux Réproduisants 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. 114-115, 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 Tech nology, 1997.
[24] A.J. Smola, B. Schölkopf, and K.-R. Müller, "The Connection between Regularization Operators and Support Vector Kernels," Neural Networks, vol. 11, no. 5, pp. 637-649, 1998.
[25] B. Schölkopf, A.J. Smola, and K.-R. Müller, "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. Svensén, 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.
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