R. Fagin, S. R. Kumar, and D. Sivakumar. Comparing top k lists. In Proc. SODA, 2003.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....w # 2 ) o(M n (d, L) Since 1 is stable, we have that d(w 1 , w # 1 ) o(M n (d, L) Since the distance measure d is a metric, or a near metric, we have that d(w 2 , w # 2 ) O(d(w 1 , w 2 ) d(w # 1 , w # 2 ) d(w 1 , w # 1 ) o (M n (d, L) 2 is stable on n . # A near metric [20] is a distance function that is reflexive, and symmetric, and satisfies the following relaxed polygonal inequality. There is a constant c independent of n, such that for all k 0, and all vectors u, w 1 , w 2 , w k , v, d(u, v) c(d(u, w 1 ) d(w 1 , w 2 ) d(w k , v) 23 ....

R. Fagin, R. Kumar, and D. Sivakumar. Comparing top k lists. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), 2003.

....nearly perfectly overlap, suggesting that in the case of PageRank, the easily calculated L1 residual is a good measure for the convergence of query result rankings. nodes (u; v) 2 U U . An analysis of various measures based on Kendall s for comparing top k lists is given by Fagin et al. in [7]. To measure the convergence of PageRank iterations in terms of induced rank orders, we measured the KDist distance between the induced rankings for the top 1,000 results, averaged across 86 test queries, using successive power iterates for the LARGEWEB dataset, with the damping factor c set to ....

....using successive power iterates for the LARGEWEB dataset, with the damping factor c set to 0.9. The average KDist values, as well as the standard residual value t , normalized so that 0 is 1, are plotted in Figure 8. Interestingly, is almost perfectly correlated with KDist. Fagin et al. show in [7] that distance measures based on Kendall s are bounded by a true metric, providing insight as to why the results of Figure 8 are to be expected. 8. RELATED WORK 8.1 Fast Eigenvector Computation The field of numerical linear algebra is a mature field, and many algorithms have been developed ....

R. Fagin, R. Kumar, and D. Sivakumar. Comparing top k lists. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms, 2003.

....measure, KSim, based on Kendall s # distance measure. Alternatively, s qd can be used as part of a more general scoring function. Several queries which produced very few hits on our repository were excluded. Note that the schemes for comparing top k lists recently proposed by Fagin et al. [13], also based on Kendall s # distance measure, di#er from KSim in the way normalization is done. Table 1. Test queries used. a#rmative action lipari alcoholism lyme disease amusement parks mutual funds architecture national parks bicycling parallel architecture blues recycling cans cheese ....

Ronald Fagin, Ravi Kumar, and D. Sivakumar. Comparing top k lists. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms, 2003.

....did not provide analytic results for the behavior of the encodings under various models for query result distributions. The use of measures based on Kendall s rank correlation for comparing document rankings has recently become popular [1, 6] and is given a thorough treatment by Fagin et al. in [2]. 7. ACKNOWLEDGMENTS I would like to thank Professor Je Ullman for his comments and feedback. I would also like to thank Mayur Datar and Aristides Gionis for comments and useful discussions on the derivations given in Section 4.2 and Appendix A. 8. ....

Ronald Fagin, Ravi Kumar, and D. Sivakumar. Comparing top k lists. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms, 2003.

....an appropriate measure of distance, between the rank orders for query results induced by Ax . We use two measures of distance for rank orders, both based on the the Kendall s rank correlation measure: the KDist measure, defined below, and the K min measure, introduced by Fagin et al. in [7]. To see if the residual is a good measure of convergence, we compared it to the KDist and K min of rankings generated by Ax . We show empirically that in the case of PageRank computations, the L1 residual k is closely correlated with the KDist and 0.01 0.1 1 0 5 10 15 20 25 30 35 40 45 ....

R. Fagin, R. Kumar, and D. Sivakumar. Comparing top k lists. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms, 2003.

....perfectly overlap, suggesting that in the case of PageRank, the easily calculated L1 residual is a good measure for the convergence of query result rankings. nodes (u; v) 2 U Theta U . An analysis of various measures based on Kendall s for comparing top k lists is given by Fagin et al. in [7]. To measure the convergence of PageRank iterations in terms of induced rank orders, we measured the KDist distance between the induced rankings for the top 1,000 results, averaged across 86 test queries, using successive power iterates for the LARGEWEB dataset, with the damping factor c set to ....

....power iterates for the LARGEWEB dataset, with the damping factor c set to 0.9. The average KDist values, as well as the standard residual value ffi t , normalized so that ffi 0 is 1, are plotted in Figure 8. Interestingly, ffi is almost perfectly correlated with KDist. Fagin et al. show in [7] that distance measures based on Kendall s are bounded by a true metric, providing insight as to why the results of Figure 8 are to be expected. 8. RELATED WORK 8.1 Fast Eigenvector Computation The field of numerical linear algebra is a mature field, and many algorithms have been developed for ....

R. Fagin, R. Kumar, and D. Sivakumar. Comparing top k lists. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms, 2003.

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R. Fagin, R. Kumar, and D. Sivakumar. Comparing top k lists. In Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 28--36, 2003.

....performance than that of C # # . Our final evaluation methodology we employ is aimed at measuring the similarity between the top k lists produced by the various ranking heuristics, and how similar the aggregation is to each one of them. Here we use the concept of comparing top k lists (see [17]) Averaged over all queries, we compare the distance of the aggregated output to each of the individual rankings given by the attributes. We also evaluate the distance between the individual rankings themselves. The particular top k distance measure we use is Kmin , which is defined as follows. ....

....Kmin , which is defined as follows. The Kmin distance between two top k lists #1 and #2 is defined to be the minimum, over all permutations #1 extending #1 and #2 extending #2 , of the Kendall tau distance between #1 and #2 , normalized to lie between 0 and 1. For further discussion of Kmin , see [17], where it is also shown that Kmin is a near metric in a precise sense. Here it su#ces to note that Kmin (#1 , #2 ) where #1 and #2 are two top k lists, achieves its minimal value of 0 if and only if #1 = #2 ; in general, values close to 0 indicate lack of disagreement between #1 and #2 , and ....

Ronald Fagin, Ravi Kumar, and D. Sivakumar. Comparing top k lists. In Proc. 14th SODA, pages 28--36, 2003.

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R. Fagin, S. R. Kumar, and D. Sivakumar. Comparing top k lists. In Proc. SODA, 2003.

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R. Fagin, R. Kumar, and D. Shivakumar. Comparing top-k lists. Proceedings of SODA, 2003.

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R. Fagin, R. Kumar, and D. Sivakumar. Comparing top k lists. In Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms, pages 28--36, 2003.

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Ronald Fagin, Ravi Kumar, and D. Sivakumar. Comparing top k lists. In Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms, pages 28--36. Society for Industrial and Applied Mathematics, 2003.

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R. Fagin, R. Kumar, and D. Sivakumar. Comparing top k lists. In Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms, pages 28--36, 2003.

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Ronald Fagin, Ravi Kumar, and D. Sivakumar. Comparing top k lists. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms, 2003.

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R. Fagin, R. Kumar, D. Sivakumar, "Comparing top k lists", SIAM J. Discrete Mathematics 17, 1 (2003), pp. 134 -- 160.

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R. Fagin, R. Kumar, and D. Shivakumar. Comparing top-k lists. Proceedings of SODA, 2003.

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R. Fagin, S. R. Kumar, and D. Sivakumar. Comparing top k lists. In Proc. SODA, 2003.

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R. Fagin, S. R. Kumar, and D. Sivakumar. Comparing top k lists. In Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Baltimore, Maryland, January 2003.

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Ronald Fagin, Ravi Kumar, and D. Sivakumar. Comparing top k lists. In Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms, pages 28--36. Society for Industrial and Applied Mathematics, 2003.

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R. Fagin, S. R. Kumar, and D. Sivakumar. Comparing top k lists. In Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Baltimore, Maryland, January 2003.

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