Aggregating inconsistent information: Ranking and clustering

Journal of the ACM

Volumn 55, Issue 5, 2008, Pages

  Ailon, Nir ^a   Charikar, Moses ^b,d   Newman, Alantha ^c  

^a GOOGLE INC   (United States)

^b PRINCETON UNIVERSITY   (United States)

^c RUTGERS UNIVERSITY   (United States)

^d Princeton University   (United States)

Author keywords

Consensus clustering; Correlation clustering; Minimum feedback arc set; Rank aggregation; Tournaments

Indexed keywords

CONSENSUS CLUSTERING; CORRELATION CLUSTERING; MINIMUM FEEDBACK ARC-SET; RANK AGGREGATION; TOURNAMENTS;

AGGLOMERATION; APPROXIMATION ALGORITHMS; CAVITY RESONATORS; POLYNOMIAL APPROXIMATION;

FLOW OF SOLIDS;

EID: 56349095491     PISSN: 00045411     EISSN: 1557735X     Source Type: Journal    
DOI: 10.1145/1411509.1411513     Document Type: Article

References (39)

1. AILON, N. 2008. Aggregation of partial rankings, p-ratings and top-m lists. Algorithmica. DOI 10.1007/S00453-008-9211-1.
2. AILON, N., AND CHARIKAR, M. 2005. Fitting tree metrics: Hierarchical clustering and phylogeny. In Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS) (Pittsburgh, PA). IEEE Computer Society Press, Los Alamitos, CA, 73-82.
3. AILON, N., CHARIKAR, M., AND NEWMAN, A. 2005. Aggregating inconsistent information: Ranking and clustering. In Proceedings of the 37th Annual Symposium on the Theory of Computing (STOC) (Boston, MA). ACM, New York, 684-693.
4. AILON, N., AND MOHRI, M. 2008. An efficient reduction of ranking to classification. In Conference on Learning Theory (COLT) (Helsinki, Finland).
5. ALON, N. 2006. Ranking tournaments. SIAM J. Disc. Math. 20, 1, 137-142.
6. ALON, N., AND SPENCER, J. H. 1992. The Probabilistic Method. Wiley, New York.
7. ARORA, S., FRIEZE, A., AND KAPLAN, H. 1996. A new rounding procedure for the assignment problem with applications to dense graph arrangement problems. In Proceedings of the 37th Annual Symposium on the Foundations of Computer Science (FOCS) (Burlington, VT). IEEE Computer Society Press, Los Alamitos, CA, 24-33.
8. BALCAN, M.-F., BANSAL, N., BEYGELZIMER, A., COPPERSMITH, D., LANGFORD, J., AND SORKIN, G. B. 2007. Robust reductions from ranking to classification. In Proceedings of the Conference on Learning Theory (COLT). Lecture Notes in Computer Science, vol. 4539. Springer-Verlag, New York, 604-619.
9. BANG-JENSEN, J., AND THOMASSEN, C. 1992. A polynomial algorithm for the 2-path problem in semicomplete graphs. SIAM J. Disc. Math. 5, 3, 366-376.
10. BANSAL, N., BLUM, A., AND CHAWLA, S. 2004. Correlation clustering. Mach. Learn. J. (Special Issue on Theoretical Advances in Data Clustering) 56, 1-3, 89-113. (Extended abstract appeared in FOCS 2002, pages 238-247.)
11. BARTHOLDI, J., TOVEY, C. A., AND TRICK, M. 1989. Voting schemes for which it can be difficult to tell who won the election. Social Choice Welf. 6, 2, 157-165.
12. BORDA, J. C. 1781. Mémoire sur les élections au scrutin. Histoire de l'Académie Royale des Sciences.
13. CAI, M.-C., DENG, X., AND ZANG, W. 200.1. An approximation algorithm for feedback vertex sets in tournaments. SIAM J. Comput. 30, 6, 1993-2007.
14. CHARIKAR, M., GURUSWAMI, V, AND WIRTH, A. 2003. Clustering with qualitative information. In Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science (FOCS) (Boston, MA). IEEE Computer Society Press, Los Alamitos, CA, 524-533.
15. CHAUDHURI, K., CHEN, K., MIHAESCU, R., AND RAO, S. 2006. On the tandem duplication-random loss model of genome rearrangement. In Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithm (SODA'06). ACM, New York, 564-570.
16. CONDORCET, M.-J. 1785. Éssai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix.
17. COPPERSMITH, D., FLEISCHER, L., AND RUDRA, A. 2006. Ordering by weighted number of wins gives a good ranking for weighted tournaments. In Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithm (SODA '06). ACM, New York, 776-782.
18. DIACONIS, P., AND GRAHAM, R. 1977. Spearman's footrule as a measure of disarray. J. Roy. Stat. Soc., Ser. B 39, 2, 262-268.
19. DINUR, I., AND SAFRA, S. 2002. On the importance of being biased. In Proceedings of the 34th Annual Symposium on the Theory of Compututing (STOC). ACM, New York, 33-42.
20. DWORK, C., KUMAR, R., NAOR, M., AND SIVAKUMAR, D. 2001a. Rank aggregation methods for the web. In Proceedings of the 10th International Conference on the World Wide Web (WWW10) (Hong Kong, China), 613-622.
21. DWORK, C., KUMAR, R., NAOR, M., AND SIVAKUMAR, D. 2001b. Rank aggregation revisited. Manuscript. (Available from: http://www.eecs.harvard.edu/~michaelm/CS222/rank2.pdf.)
22. EVEN, G., NAOR, J. S., SUDAN, M., AND SCHIEBER, B. 1998. Approximating minimum, feedback sets and multicuts in directed graphs. Algorithmica 20, 2, 151-174.
23. FAGIN, R., KUMAR, R., AND SIVAKUMAR, D. 2003. Efficient similarity search and classification via rank aggregation. In Proceedings of the 2003 ACM SIGMOD International Conference on Management of Data (San Diego, CA). ACM, New York, 301-312.
24. FILKOV, V, AND SKIENA, S. 2003. Integrating microarray data by consensus clustering. In Proceedings of International Conference on Tools with Artificial Intelligence (ICTAI) (Sacramento, CA). 418-425.
25. FRIEZE, A., AND KANNAN, R. 1999. Quick approximations to matrices and applications. Combinatorica 19, 2, 175-220.
26. GIONIS, A., MANNILA, H., AND TSAPARAS, P. 2005. Clustering aggregation. In Proceedings of the 21st International Conference on Data Engineering (ICDE) (Tokyo, Japan).
27. HÄSTAD, J. 2001. Some optimal inapproximability results. J. ACM 48, 798-859.
28. KARP, R. M. 1972. Reducibility among combinatorial problems. In Complexity of Computer Computations. Plenum Press, New York, 85-104.
29. KEMENY, J. G. 1959. Mathematics without numbers. Daedalus 88, 571-591.
30. KEMENY, J., AND SNELL, J. 1962. Mathematical Models in the Social Sciences. Blaisdell, New York. (Reprinted by MIT Press, Cambridge, 1972.)
31. KENYON-MATHIEU, C., AND SCHUDY, W. 2007. How to rank with few errors. In Proceedings of the 39th Annual ACM Symposium on Theory of Computing (STOC) (New York, NY). ACM, New York, 95-103.
32. NEWMAN, A. 2000. Approximating the maximum acyclic subgraph. M.S. thesis, Massachusetts Institute of Technology, Cambridge, MA.
33. NEWMAN, A., AND VEMPALA, S. 2001. Fences are futile: On relaxations for the linear ordering problem. In Proceedings of the 8th Conference on Integer Programming and Combinatorial Optimization (IPCO). 333-347.
34. POTTS, C. N. 1980. An algorithm for the single machine sequencing problem with precedence constraints. Math. Prog. 13, 78-87.
35. SEYMOUR, P. 1995. Packing directed circuits fractionally. Combinatorica 15, 281-288.
36. SPECKENMEYER, E. 1989. On feedback problems in digraphs. Graph Theoretic Concepts in Computer Science, Lecture Notes in Computer Science, vol. 411, Springer-Verlag, New York, 218-231.
37. STREHL, A. 2002. PhD dissertation. Ph.D. thesis, University of Texas at Austin.
38. WAKABAYASHI, Y. 1998. The complexity of computing medians of relations. Resenhas 3, 3, 323-349.
39. WILLIAMSON, D. P., AND VAN ZUYLEN, A. 2007. Deterministic algorithms for rank aggregation and other ranking and clustering problems. In Proceedings of the 5th Workshop on Approximation and Online Algorithms (WAOA).