Online Pairwise Ranking Based on Graph Edge–Connectivity
Conference paper
First Online:
Abstract
We propose a novel ranking algorithm that takes into account specific properties of the graph that represents the items and the user votes in pairwise comparison scenarios. The algorithm models the scoring relationships between instances as local edges among vertices in a corresponding graph and use such properties to find scores for each instance. We have compared the performance of the algorithm with other widely known information retrieval techniques tasked with ranking a set of movies. As a baseline implementation, we have used the topological ordering of the acyclic subgraph with maximum weight, by solving an approximated version of the maximum acyclic subgraph problem. The results show accurate ranking lists for the movie dataset.
Keywords
Online ranking MASP Vertex–connectivity Machine learningReferences
- 1.Jiang, X., Lim, L.-H., Yao, Y., Ye, Y.: Statistical ranking and combinatorial hodge theory. In: Mathematical Programming (2011)Google Scholar
- 2.Sreenivas, G., Rina, P., Sarma, A.D., Atish, D.S.: Ranking mechanisms in twitter-like forums. In: Proceedings of the Third ACM International Conference on Web Search and Data Mining, pp. 21–30, 2010Google Scholar
- 3.Hochbaum, Dorit S., Levin, Asaf: Methodologies and algorithms for group-rankings decision. Manage. Sci. 52, 1394–1408 (2006)CrossRefGoogle Scholar
- 4.Large Margin Rank Boundaries for Ordinal Regression, chapter 7, pp. 115–132. MIT Press (2000)Google Scholar
- 5.Freund, Yoav, Iyer, Raj, Schapire, Robert E., Singer, Yoram: An efficient boosting algorithm for combining preferences. J. Mach. Learn. Res. 4, 933–969 (2003)MathSciNetMATHGoogle Scholar
- 6.Karp, R.M.: Reducibility among combinatorial problems. Complexity Comput. Comput. (1972)Google Scholar
- 7.Lucchesi, C.L.: A minimax equality for directed graphs. Ph.D. thesis, University of Waterloo (1976)Google Scholar
- 8.Charikar, M., Makarychev, K., Makarychev, Y.: On the advantage over random for maximum acyclic subgraph. In: 48th Annual IEEE Symposium on Foundations of Computer Science, pp. 625–633 (2007)Google Scholar
- 9.Haeupler, B., Kavitha, T., Mathew, R., Sen, S., Tarjan, R.E.: Faster algorithms for incremental topological ordering. In: Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I, pp. 421–433. Springer, Berlin (2008)Google Scholar
- 10.Hassin, Refael, Rubinstein, Shlomi: Approximations for the maximum acyclic subgraph problem. Inf. Process. Lett. 51, 133–140 (1994)MathSciNetCrossRefMATHGoogle Scholar
- 11.Khot, S., O’Donnell, R.: Sdp gaps and ugc-hardness for maxcutgain. In: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science, pp. 217–226. IEEE Computer Society, Washington, DC, USA (2006)Google Scholar
- 12.Noga, A., Assaf, N.: Approximating the cut-norm via grothendieck’s inequality. In: Proceedings of the Thirty-sixth Annual ACM Symposium on Theory of Computing, STOC ’04, pp. 72–80. ACM, New York, NY, USA, (2004)Google Scholar
- 13.Ulrok B., Thomas, E.: Network Analysis. Springer (2005)Google Scholar
- 14.Lawrence, P., Sergey, B., Rajeev, M., Winograd, T.: Bringing order to the web. Stanford Digital Library project, talk, the pagerank citation ranking (1999)Google Scholar
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