Attributed hypergraph matching on a Riemannian manifold

If we consider a matching that preserves high-order relationships among points in the same set, we can int-roduce a hypergraph-matching technique to search for correspondence according to high-order feature values. While graph matching has been widely studied, there is limited research available regarding hypergraph matching. In this paper, we formulate hypergraph matching in terms of tensors. Then, we reduce the hypergraph matching to a bipartite matching problem that can be solved in polynomial time. We then extend this hypergraph matching to attributed hypergraph matching using a combination of different attributes with different orders. We perform analyses that demonstrate that this method is robust when handling noisy or missing data and can achieve inexact graph matching. To the best of our knowledge, while attributed graph-matching and hypergraph-matching have been heavily researched, methods for attributed hypergraph matching have not been proposed before.

[1]  Minsu Cho,et al.  Reweighted Random Walks for Graph Matching , 2010, ECCV.

[2]  Shihui Ying,et al.  A New Approach to Weighted Graph Matching , 2009, IEICE Trans. Inf. Syst..

[3]  Horst Bunke,et al.  Matching of Hypergraphs - Algorithms, Applications, and Experiments , 2008, Applied Pattern Recognition.

[4]  Yosi Keller,et al.  Efficient High Order Matching , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  Mario Vento,et al.  A (sub)graph isomorphism algorithm for matching large graphs , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  Kaspar Riesen,et al.  Exact and Inexact Graph Matching: Methodology and Applications , 2010, Managing and Mining Graph Data.

[7]  Mario Vento,et al.  Thirty Years Of Graph Matching In Pattern Recognition , 2004, Int. J. Pattern Recognit. Artif. Intell..

[8]  Tamara G. Kolda,et al.  Tensor Decompositions and Applications , 2009, SIAM Rev..

[9]  David M. Skapura,et al.  Neural networks - algorithms, applications, and programming techniques , 1991, Computation and neural systems series.

[10]  Sei-Wang Chen,et al.  Video stabilization for a hand-held camera based on 3D motion model , 2009, 2009 16th IEEE International Conference on Image Processing (ICIP).

[11]  Sargur N. Srihari,et al.  Decision Combination in Multiple Classifier Systems , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  Tariq S. Durrani,et al.  A RKHS Interpolator-Based Graph Matching Algorithm , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  Cristian Sminchisescu,et al.  Semi-supervised learning and optimization for hypergraph matching , 2011, 2011 International Conference on Computer Vision.

[14]  Edwin R. Hancock,et al.  Inexact graph matching using genetic search , 1997, Pattern Recognit..

[15]  Steven Gold,et al.  A Graduated Assignment Algorithm for Graph Matching , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  Charu C. Aggarwal,et al.  Managing and Mining Graph Data , 2010, Managing and Mining Graph Data.

[17]  Mohammad Abdulkader Abdulrahim,et al.  Parallel algorithms for labeled graph matching , 1998 .

[18]  B. D. Mckay,et al.  Practical graph isomorphism, Numerical mathematics and computing, Proc. 10th Manitoba Conf., Winnipeg/Manitoba 1980 , 1981 .

[19]  H. Kuhn.  The Hungarian method for the assignment problem , 1955 .

[20]  Shinji Umeyama,et al.  An Eigendecomposition Approach to Weighted Graph Matching Problems , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[21]  Mauro Dell'Amico,et al.  Assignment Problems , 1998, IFIP Congress: Fundamentals - Foundations of Computer Science.

[22]  Christos H. Papadimitriou,et al.  Computational complexity , 1993 .

[23]  Robert M. Haralick,et al.  Structural Descriptions and Inexact Matching , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[24]  Fritz Wysotzki,et al.  Solving inexact graph isomorphism problems using neural networks , 2005, Neurocomputing.

[25]  I. S. Filotti,et al.  A polynomial-time algorithm for determining the isomorphism of graphs of fixed genus , 1980, STOC '80.

[26]  Brendan D. McKay,et al.  Practical graph isomorphism, II , 2013, J. Symb. Comput..

[27]  Jean Ponce,et al.  A tensor-based algorithm for high-order graph matching , 2009, 2009 IEEE Conference on Computer Vision and Pattern Recognition.

[28]  Jing-Yu Yang,et al.  A graph decomposition approach to least squares attributed graph matching , 2004, Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004..

[29]  Douglas M. Campbell,et al.  Tree Isomorphism Algorithms: Speed vs. Clarity , 1991 .

[30]  Edwin R. Hancock,et al.  Structural Matching by Discrete Relaxation , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[31]  Sylvie Philipp-Foliguet,et al.  Inexact graph matching based on kernels for object retrieval in image databases , 2011, Image Vis. Comput..

[32]  Peter Norvig,et al.  Artificial Intelligence: A Modern Approach , 1995 .

[33]  Minsu Cho,et al.  Hyper-graph matching via reweighted random walks , 2011, CVPR 2011.

[34]  King-Sun Fu,et al.  Error-Correcting Isomorphisms of Attributed Relational Graphs for Pattern Analysis , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[35]  Martial Hebert,et al.  A spectral technique for correspondence problems using pairwise constraints , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[36]  Julian R. Ullmann,et al.  An Algorithm for Subgraph Isomorphism , 1976, J. ACM.

[37]  Amnon Shashua,et al.  Probabilistic graph and hypergraph matching , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[38]  Horst Bunke.  Error-Tolerant Graph Matching: A Formal Framework and Algorithms , 1998, SSPR/SPR.

[39]  Edwin R. Hancock,et al.  Structural Graph Matching Using the EM Algorithm and Singular Value Decomposition , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[40]  Mauro Dell'Amico,et al.  8. Quadratic Assignment Problems: Algorithms , 2009 .

[41]  Uriel Feige,et al.  Approximating Maximum Clique by Removing Subgraphs , 2005, SIAM J. Discret. Math..

[42]  Dennis K. J. Lin,et al.  A measurement of multi-factor orthogonality , 1996 .