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Comparing Top k Lists

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Kumar, Ravi Sivakumar, D. Fagin, Ronald
Copyright Year	2003
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 they are "almost" a metric in the following two seemingly unrelated aspects:(i) they satisfy a relaxed version of the polygonal (hence, triangle) inequality, and(ii) there is a metric with positive constant multiples that bound 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. (A correction for this article has been appended to the pdf file.)
Starting Page	134
Ending Page	160
Page Count	27
File Format	PDF
ISSN	08954801
DOI	10.1137/S0895480102412856
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	1
Volume Number	17
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-08-01
Access Restriction	Subscribed
Subject Keyword	top k list polygonal inequality metric triangle inequality near metric distance measures Approximation algorithms rank aggregation Combinatorics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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