A polynomial characterization of hypergraphs using the Ihara zeta function

Pattern Recognition

Volumn 44, Issue 9, 2011, Pages 1941-1957

  Ren, Peng ^a   Aleksić, Tatjana ^b   Wilson, Richard C ^a   Hancock, Edwin R ^a  

^a UNIVERSITY OF YORK   (United Kingdom)

^b UNIVERSITY OF KRAGUJEVAC   (Serbia)

Author keywords

Hypergraph characterization; Ihara coefficients; Spectral analysis

Indexed keywords

CARDINALITIES; EFFICIENT METHOD; EXPERIMENTAL EVALUATION; HYPER GRAPH; HYPERGRAPH CHARACTERIZATION; IHARA COEFFICIENTS; LAPLACIANS; POLYNOMIAL COEFFICIENTS; RELATIONAL STRUCTURES; SPECTRAL ANALYSIS; SPECTRAL CHARACTERIZATION; ZETA FUNCTION;

CHARACTERIZATION; FUNCTIONS; LAPLACE TRANSFORMS; POLYNOMIALS; SPECTRUM ANALYSIS; SPECTRUM ANALYZERS;

GRAPH THEORY;

EID: 79957500663     PISSN: 00313203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.patcog.2010.06.011     Document Type: Conference Paper

References (39)

1. S. Agarwal, J. Lim, L. Zelnik-Manor, P. Perona, D. Kriegman, and S. Belongie Beyond pairwise clustering Proceedings of IEEE Conference on Computer Vision and Pattern Recognition 2005 838 845
2. S. Agarwal, K. Branson, and S. Belongie Higher-order learning with graphs Proceedings of the International Conference on Machine Learning 2006 17 24
3. H. Bass The IharaSelberg zeta function of a tree lattice International Journal of Mathematics 6 1992 717 797
4. M. Bolla Spectra, Euclidean representations and clusterings of hypergraphs Discrete Mathematics 117 1993
5. A. Bretto, H. Cherifi, and D. Aboutajdine Hypergraph imaging: an overview Pattern Recognition 35 3 2001 651 658 (Pubitemid 34034602)
6. H. Bunke, P. Dickinson, M. Neuhaus, and M. Stettler Matching of hypergraphs - algorithms, applications, and experiments Studies in Computational Intelligence 91 2008 131 154
7. T.S. Caetano, J.J. McAuley, L. Cheng, Q.V. Le, A.J. Smola, and S. Clara Learning graph matching IEEE Transactions on Pattern Analysis and Machine Intelligence 31 6 2009 1048 1058
8. G. Chen, and G. Lerman Spectral curvature clustering (SCC) International Journal of Computer Vision 81 3 2009 317 330
9. G. Chen, and G. Lerman Foundations of a multi-way spectral clustering framework for hybrid linear modeling Journal of Foundations of Computational Mathematics 9 2009 517 558
10. G. Chen, S. Atev, and G. Lerman Kernel spectral curvature clustering (KSCC) Proceedings of International Workshop on Dynamical Vision 2009
11. F. Chung The Laplacian of a hypergraph AMS DIMACS Series in Discrete Mathematics and Theoretical Computer Science 10 1993 21 36
12. O. Duchenne, F.R. Bach, I.S. Kweon, and J. Ponce A tensor-based algorithm for high-order graph matching Proceedings of IEEE Conference on Computer Vision and Pattern Recognition 2009 1980 1987
13. D. Gibson, J. Kleinberg, and P. Raghavan Clustering categorical data: an approach based on dynamical systems VLDB Journal 8 4-3 2000 222 236
14. V.M. Govindu A tensor decomposition for geometric grouping and segmentation Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition 2005 1150 1157 (Pubitemid 43897322)
15. L. Hagen, and A.B. Kahng New spectral methods for ratio cut partitioning and clustering IEEE Transactions on Computed-Aided Design of Integrated Circuits and Systems 11 9 1992 1074 1085 (Pubitemid 23555831)
16. C.G. Harris, and M.J. Stephens A combined corner and edge detector Proceedings of the Fourth Alvey Vision Conference 1994 147 151
17. X. He, D. Cai, and P. Niyogi Tensor subspace analysis Proceedings of Advances in Neural Information Processing Systems 2005
18. X. He, D. Cai, H. Liu, and J. Han Image clustering with tensor representation Proceedings of ACM Multimedia 2005 132 140
19. Z. He, A. Cichocki, S. Xie, K. Choi, Detecting the number of clusters in n-way probabilistic clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence, to appear.
20. kφ ) Proceedings of Symposium on Pure Mathematics 1965 272 278
21. Y. Ihara On discrete subgroups of the two by two projective linear group over p-adic fields Journal of Mathematics Society Japan 18 1966 219 235
22. M. Kotani, and T. Sunada Zeta functions of finite graphs Journal of Mathematical Sciences, The University of Tokyo 7 1 2000 7 25
23. W. Li, and P. Sole Spectra of regular graphs and hypergraphs and orthogonal polynomials European Journal of Combinatorics 17 1996 461 477 (Pubitemid 126375778)
24. A. Oliva, and A. Torralba Modeling the shape of the scene: a holistic representation of the spatial envelope International Journal of Computer Vision 42 3 2001 145 175 (Pubitemid 32680801)
25. P. Ren, R.C. Wilson, and E.R. Hancock Spectral embedding of feature hypergraphs Proceedings of Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition 2008 257 266
26. P. Ren, T. Aleksić, R.C. Wilson, and E.R. Hancock Hypergraphs, characteristic polynomials and the Ihara zeta function Proceedings of the International Conference on Computer Analysis of Images and Patterns 2009 369 376
27. J.A. Rodriguez On the Laplacian eigenvalues and metric parameters of hypergraphs Linear and Multilinear Algebra 51 2003 285 297 (Pubitemid 36989620)
28. S. Rota Bulo, A. Albarelli, M. Pelillo, and A. Torsello A hypergraph-based approach to affine parameters estimation Proceedings of the International Conference on Pattern Recognition 2008
29. S. Rota Bulo, and M. Pelillo A game-theoretic approach to hypergraph clustering Proceedings of Advances in Neural Information Processing Systems 2009 1571 1579
30. G. Scott, and C.K. Storm The coefficients of the Ihara zeta function Involve - A Journal of Mathematics 1 2 2008 217 233
31. A. Shashua, and A. Levin Linear image coding for regression and classification using the tensor-rank principle Proceedings of IEEE Conference on Computer Vision and Pattern Recognition 2001 623 630
32. A. Shashua, R. Zass, and T. Hazan Multi-way clustering using super-symmetric non-negative tensor factorization Proceedings of the European Conference on Computer Vision 2006 595 608 (Pubitemid 44029661)
33. C.K. Storm The zeta function of a hypergraph Electronic Journal of Combinatorics 13 2006
34. M.A.O. Vasilescu, and D. Terzopoulos Multilinear analysis of image ensembles: TensorFaces Proceedings of the European Conference on Computer Vision 2002 447 460
35. R.C. Wilson, and P. Zhu A study of graph spectra for comparing graphs and trees Pattern Recognition 41 9 2008 2833 2841
36. A.K.C. Wong, S.W. Lu, and M. Rioux Recognition and shape synthesis of 3D objects based on attributed hypergraphs IEEE Transactions on Pattern Analysis and Machine Intelligence 11 3 1989 279 290
37. S. Yan, D. Xu, Q. Yang, L. Zhang, X. Tang, and H.J. Zhang Discriminant analysis with tensor representation Proceedings of IEEE Conference on Computer Vision and Pattern Recognition 2005 526 532
38. R. Zass, and A. Shashua Probabilistic graph and hypergraph matching Proceedings of IEEE Conference on Computer Vision and Pattern Recognition 2008
39. D. Zhou, J. Huang, and B. Scholkopf Learning with hypergraphs: clustering, classification, and embedding Proceedings of Advances in Neural Information Processing Systems 2007 1601 1608