Szemerédi's regularity lemma and its applications to pairwise clustering and segmentation

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4679 LNCS, Issue , 2007, Pages 13-27

  Sperotto, Anna ^a   Pelillo, Marcello ^b  

^a UNIVERSITY OF TWENTE   (Netherlands)

^b CA' FOSCARI UNIVERSITY OF VENICE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CLASSIFICATION (OF INFORMATION); CONFORMAL MAPPING; GRAPH THEORY; IMAGE SEGMENTATION; PATTERN RECOGNITION;

ARBITRARY GRAPHS; PATTERN RECOGNITION PROBLEMS;

CLUSTERING ALGORITHMS;

EID: 38149134458     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-74198-5_2     Document Type: Conference Paper

References (16)

1. Alon, N., Duke, R.A., Lefmann, H., Rödl, V., Yuster, R.: The algorithmic aspects of the regularity lemma. J. of Algorithms, vol. 16, pp. 80-109 (1994) Also, Proc. 33rd IEEE FOCS, Pittsburgh, IEEE, 473-481 (1992)
2. Bengio, Y., Paiement, J., Vincent, P., Delalleau, O., Roux, N.L., Ouimet, M.: Outof-sample extensions for lle, isomap, mds, eigenmaps, and spectral clustering. In: Thrun, S., Saul, L., Schölkopf, B. (eds.) Advances in Neural Information Processing Systems 16, MIT Press, Cambridge, MA (2004)
3. Bollobás, B.: Extremal Graph Theory. Academic Press, London (1978)
4. Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge, MA (2001)
5. Czygrinow, A., Rödl, V.: An algorithmic regularity lemma for hypergraphs. SIAM .1. Comput. 30(4), 1041-1066 (2000)
6. Diestel, R.: Graph Theory, 3rd edn. Springer, New York (2005)
7. Fowlkes, C., Belongie, S., Chung, F.R.K., Malik, J.: Spectral grouping using the Nyström method. IEEE Trans. Pattern Anal. Mach. Intell. 26, 214-225 (2004)
8. Frieze, A.M., Kannan, R.: A simple algorithm for constructing Szemerédi's regularity partition. Electron. J. Comb. 6 (1999)
9. Kohayakawa, Y., Rödl, V., Thoma, L.: An optimal algorithm for checking regularity. SIAM J. Comput. 32(5), 1210-1235 (2003)
10. Komlós, J., Shokoufandeh, A., Simonovits, M., Szemerédi, E.: The regularity lemma and its applications in graph theory. In: Khosrovshahi, G.B., Shokoufandeh, A., Shokrollahi, A. (eds.) Theoretical Aspects of Computer Science: Advanced Lectures, pp. 84-112. Springer, New York (2002)
11. Komlós, J., Simonovits, M.: Szemerédi's regularity lemma and its applications in graph theory. In: Miklós, D., Szonyi, T., Sós, V.T. (eds.) Combinatorics, Paul Erdös is Eighty (Vol. 2), pp. 295-352. Bolyai Society Mathematical Studies 2, Budapest (1996)
12. Motzkin, T.S., Straus, E.G.: Maxima for graphs and a new proof of a theorem of Turan. Canad. J. Math. 17, 533-540 (1965)
13. Pavan, M., Pelillo, M.: Dominant sets and pairwise clustering. IEEE Trans. Pattern Anal. Mach. Intell. 29, 167-172 (2007)
14. Pavan, M., Pelillo, M.: Efficient out-of-sample extension of dominant-set clusters. In: Saul, L.K., Weiss, Y., Bottou, L. (eds.) Advances in Neural Information Processing Systems 17, pp. 1057-1064. MIT Press, Cambridge, MA (2005)
15. Roth, V., Laub, J., Kawanabe, M., Buhmann, J.M.: Optimal cluster preserving embedding of nonmetric proximity data. IEEE Trans. Pattern Anal. Mach. Intell. 25, 1540-1551 (2003)
16. Szemerédi, E.: Regular partitions of graphs. In: Colloques Internationaux CNRS 260- -Problèmes Combinatoires et Théorie des Graphes, Orsay, pp. 399-401 (1976)