Dense subgraph partition of positive hypergraphs

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn 37, Issue 3, 2015, Pages 541-554

  Liu, Hairong ^a   Latecki, Longin Jan ^b   Yan, Shuicheng ^c  

^a Purdue University   (United States)

^b Temple University   (United States)

^c NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

dense subgraph; densest k subgraph; Graph partition; image matching; mode seeking

Indexed keywords

ALGORITHMS; EVOLUTIONARY ALGORITHMS; IMAGE MATCHING;

DENSE SUBGRAPH; DENSEST K SUBGRAPH; DIVIDE-AND-CONQUER ALGORITHM; EVOLUTION ALGORITHMS; GRAPH PARTITION; GRAPHS AND HYPERGRAPHS; MODE SEEKING; PARALLEL PROCESSING;

GRAPH THEORY;

EID: 84923062574     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.2014.2346173     Document Type: Article

References (42)

1. P. Fjällström, "Algorithms for graph partitioning: A survey," Comput. Inf. Sci., vol. 3, no. 10, pp. 143-179, 1998.
2. th Annu. Des. Autom. Conf., 1997, pp. 526-529.
3. K. Andreev and H. Racke, "Balanced graph partitioning," Theory Comput. Syst., vol. 39, no. 6, pp. 929-939, Aug. 2006.
4. M. Newman, "Modularity and community structure in networks," Proc. Nat. Acad. Sci., vol. 103, no. 23, pp. 8577-8582, 2006.
5. J. Shi and J. Malik, "Normalized cuts and image segmentation,"IEEE Trans. Pattern Anal. Mach. Intell., vol. 22, no. 8, pp. 888-905, Aug. 2000.
6. S. Khuller and B. Saha, "On finding dense subgraphs," in Proc. Automata Languages Program., 2009, pp. 597-608.
7. U. Feige, G. Kortsarz, and D. Peleg, "The dense k-subgraph problem,"Algorithmica, vol. 29, pp. 410-421, 2001.
8. B. Kernighan and S. Lin, "An efficient heuristic procedure for partitioning graphs," Bell Syst. Tech. J., vol. 49, pp. 291-307, 1970.
9. D.-H. Huang and A. B. Kahng, "When clusters meet partitions: New density-based methods for circuit decomposition," in Proc. Eur. Conf. Des. Test, 1995, pp. 60-64.
10. I. Dhillon, Y. Guan, and B. Kulis, "Kernel k-means: spectral clustering and normalized cuts," in Proc. ACM Int. Conf. Knowl. Discov. Data Min., 2004, pp. 551-556.
11. V. Kolmogorov and R. Zabin, "What energy functions can be minimized via graph cuts?" IEEE Trans. Pattern Anal. Mach. Intell., vol. 26, no. 2, pp. 147-159, Jun. 2004.
12. C. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity. Mineola, NY, USA: Dover, 1998.
13. J. H. Kappes, M. Speth, B. Andres, G. Reinelt, and C. Schn, "Globally optimal image partitioning by multicuts," in Proc. Energy Minim. Methods Comput. Vis. Pattern Recognit., 2011, pp. 31-44.
14. th Conf. Des. Autom., 1982, pp. 175-181.
15. D. Zhou, J. Huang, and B. Schölkopf, "Learning with hypergraphs: Clustering, classification, and embedding," in Proc. Adv. Neural Inf. Process. Syst., 2006, pp. 1601-1608.
16. J. Rodríguez, "Laplacian eigenvalues and partition problems in hypergraphs," Appl. Math. Letters, vol. 22, no. 6, pp. 916-921, 2009.
17. G. Karypis and V. Kumar, "A fast and high quality multilevel scheme for partitioning irregular graphs," SIAM J. Sci. Comput., vol. 20, no. 1, pp. 359-392, 1998.
18. N. Bansal, A. Blum, and S. Chawla, "Correlation clustering,"Mach. Learn., no. 1-3, vol. 56, pp. 89-113, 2004.
19. th Annu. Eur. Symp. Algorithms, 2003, pp. 208-220.
20. S. Kim, S. Nowozin, P. Kohli, and C. D. Yoo, "Higher-order correlation clustering for image segmentation," in Proc. Adv. Neural Inf. Process. Syst., 2011, pp. 1530-1538.
21. P. F. Felzenszwalb and D. P. Huttenlocher, "Efficient graph-based image segmentation," Int. J. Comput. Vis., vol. 59, no. 2, pp. 167-181, 2004.
22. D. Gibson, R. Kumar, and A. Tomkins, "Discovering large dense subgraphs in massive graphs," in Proc. Int. Conf. Very Large Data Bases, 2005, pp. 721-732.
23. H. Liu and S. Yan, "Robust graph mode seeking by graph shift,"in Proc. Int. Conf. Mach. Learn., 2010, pp. 671-678.
24. H. Liu, L. Latecki, and S. Yan, "Fast detection of dense subgraph with iterative shrinking and expansion," IEEE Trans. Pattern Anal. Mach. Intell., vol. 35, no. 9, pp. 2131-2142, 2013.
25. J. Chen and Y. Saad, "Dense subgraph extraction with application to community detection," IEEE Trans. Knowl. Data Eng., vol. 24, no. 7, pp. 1216-1230, Jul. 2012.
26. M. Pavan and M. Pelillo, "Dominant sets and pairwise clustering," IEEE Trans. Pattern Anal. Mach. Intell., vol. 29, no. 1, pp. 167-172, Jan. 2007.
27. A. Goldberg, Finding a Maximum Density Subgraph, University of California Berkeley, CA, 1984.
28. S. R. Bulö and M. Pelillo, "A game-theoretic approach to hypergraph clustering," IEEE Trans. Pattern Anal. Mach. Intell., vol. 35, no. 6, pp. 1312-1327, Apr. 2013.
29. B. Saha, A. Hoch, S. Khuller, L. Raschid, and X.-N. Zhang, "Dense subgraphs with restrictions and applications to gene annotation graphs," in Proc. Res. Comput. Mol. Biol., 2010, pp. 456-472.
30. F. Porikli, "Integral histogram: A fast way to extract histograms in cartesian spaces," in Proc. IEEE Conf. Comput. Vis. Pattern Recognit., 2005, vol. 1, pp. 829-836.
31. P. Hammer, P. Hansen, and B. Simeone, "Roof duality, complementation and persistency in quadratic 0-1 optimization," Math. Program., vol. 28, no. 2, pp. 121-155, 1984.
32. H. Ishikawa, "Transformation of general binary mrf minimization to the first-order case," IEEE Trans. Pattern Anal. Mach. Intel., vol. 33, no. 6, pp. 1234-1249, Apr. 2011.
33. E. Boros, P. Hammer, and X. Sun, "Network flows and minimization of quadratic pseudo-boolean functions," Tech. Rep. RRR 17-1991, 1991.
34. L. M. Manevitz and M. Yousef, "One-class svms for document classification," J. Mach. Learn. Res., vol. 2, pp. 139-154, 2002.
35. X. Yuan and T. Zhang, "Truncated power method for sparse eigenvalue problems," J. Mach. Learn. Res., vol. 14, pp. 899-925, 2013.
36. A. Y. Ng, M. I. Jordan, Y. Weiss, "On spectral clustering: Analysis and an algorithm," Adv. Neural Inf. Process. Syst., vol. 2, pp. 849-856, 2002.
37. F. Lin and W. W. Cohen, "Power iteration clustering," in Proc. Int. Conf. Mach. Learn., vol. 10, 2010, pp. 655-662.
38. R. Zass and A. Shashua, "Probabilistic graph and hypergraph matching," in Proc. IEEE Conf. Comput. Vis. Pattern Recog., 2008, pp. 1-8.
39. O. Duchenne, F. Bach, I.-S. Kweon, and J. Ponce, "A tensor-based algorithm for high-order graph matching," IEEE Trans. Pattern Anal. Mach. Intell., vol. 33, no. 12, pp. 2383-2395, Dec. 2011.
40. J. Lee, M. Cho, and K. M. Lee, "Hypergraph matching via reweighted random walks," in Proc. IEEE Conf. Comput. Vis. Pattern Recogn., 2011, pp. 1633-1640.
41. D. G. Lowe, "Distinctive image features from scale-invariant keypoints,"Int. J. Comput. Vis., vol. 60, no. 2, pp. 91-110, 2004.
42. G. Karypis and V. Kumar, "hmetis: A hypergraph partitioning package, version 1.5. 3," 1998.