%0 Conference Paper %1 fagin03top %A Fagin, Ronald %A Kumar, Ravi %A Sivakumar, D. %B SODA '03: Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms %C Philadelphia, PA, USA %D 2003 %I Society for Industrial and Applied Mathematics %K evaluation kendall list no-groundtruth ranking search spearman %P 28--36 %T Comparing top k lists %U http://portal.acm.org/citation.cfm?id=644113&dl=ACM&coll=GUIDE %X Motivated by several applications, we introduce various distance measures between "top k lists." Some of these distance measures are metrics, while others are not. For each of these latter distance measures: we show that it is älmost" a metric in the following two seemingly unrelated aspects:step-(i) it satisfies a relaxed version of the polygonal (hence, triangle) inequality, andstep-(ii) there is a metric with positive constant multiples that bounds our measure above and below.This is not a coincidence---we show that these two notions of almost being a metric are the same. Based on the second notion, we define two distance measures to be equivalent if they are bounded above and below by constant multiples of each other. We thereby identify a large and robust equivalence class of distance measures.Besides the applications to the task of identifying good notions of (dis-)similarity between two top k lists, our results imply polynomial-time constant-factor approximation algorithms for the rank aggregation problem with respect to a large class of distance measures. %@ 0-89871-538-5

@inproceedings{fagin03top, abstract = {Motivated by several applications, we introduce various distance measures between "top k lists." Some of these distance measures are metrics, while others are not. For each of these latter distance measures: we show that it is "almost" a metric in the following two seemingly unrelated aspects:step-(i) it satisfies a relaxed version of the polygonal (hence, triangle) inequality, andstep-(ii) there is a metric with positive constant multiples that bounds our measure above and below.This is not a coincidence---we show that these two notions of almost being a metric are the same. Based on the second notion, we define two distance measures to be equivalent if they are bounded above and below by constant multiples of each other. We thereby identify a large and robust equivalence class of distance measures.Besides the applications to the task of identifying good notions of (dis-)similarity between two top k lists, our results imply polynomial-time constant-factor approximation algorithms for the rank aggregation problem with respect to a large class of distance measures.}, added-at = {2007-07-02T18:10:50.000+0200}, address = {Philadelphia, PA, USA}, author = {Fagin, Ronald and Kumar, Ravi and Sivakumar, D.}, biburl = {https://www.bibsonomy.org/bibtex/2f0687a95aa8a9d30c3890800f1c8f6a6/beate}, booktitle = {SODA '03: Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms}, description = {Comparing top k lists}, interhash = {5a06753274ed386b177b0c4db7d61c01}, intrahash = {f0687a95aa8a9d30c3890800f1c8f6a6}, isbn = {0-89871-538-5}, keywords = {evaluation kendall list no-groundtruth ranking search spearman}, location = {Baltimore, Maryland}, pages = {28--36}, publisher = {Society for Industrial and Applied Mathematics}, timestamp = {2011-02-10T12:23:49.000+0100}, title = {Comparing top k lists}, url = {http://portal.acm.org/citation.cfm?id=644113&dl=ACM&coll=GUIDE}, year = 2003 }