article

Comparing Top k Lists

Authors:

Ronald Fagin,

Ravi Kumar,

D. SivakumarAuthors Info & Claims

SIAM Journal on Discrete Mathematics, Volume 17, Issue 1

Pages 134 - 160

https://doi.org/10.1137/S0895480102412856

Published: 01 January 2004 Publication History

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.

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Campbell FStoyanovich JMoskovitch Y(2024)Rodeo: Making Refinements for Diverse Top-K QueriesProceedings of the VLDB Endowment10.14778/3685800.368587017:12(4341-4344)Online publication date: 1-Aug-2024
https://dl.acm.org/doi/10.14778/3685800.3685870
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Corsi MUrbano JSakai TIshita EOhshima HRadboud FMao JJose J(2024)How do Ties Affect the Uncertainty in Rank-Biased Overlap?Proceedings of the 2024 Annual International ACM SIGIR Conference on Research and Development in Information Retrieval in the Asia Pacific Region10.1145/3673791.3698422(125-134)Online publication date: 8-Dec-2024
https://dl.acm.org/doi/10.1145/3673791.3698422
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Published In

cover image SIAM Journal on Discrete Mathematics

SIAM Journal on Discrete Mathematics Volume 17, Issue 1

January 2004

169 pages

ISSN:0895-4801

Issue’s Table of Contents

Publisher

Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 January 2004

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Campbell FStoyanovich JMoskovitch Y(2024)Rodeo: Making Refinements for Diverse Top-K QueriesProceedings of the VLDB Endowment10.14778/3685800.368587017:12(4341-4344)Online publication date: 1-Aug-2024
https://dl.acm.org/doi/10.14778/3685800.3685870
Pethes RBodor-Eranus ETakács KKovács L(2024)The Core Might Change Anyhow We Define ItComplexity10.1155/2024/39568772024Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1155/2024/3956877
Corsi MUrbano JSakai TIshita EOhshima HRadboud FMao JJose J(2024)How do Ties Affect the Uncertainty in Rank-Biased Overlap?Proceedings of the 2024 Annual International ACM SIGIR Conference on Research and Development in Information Retrieval in the Asia Pacific Region10.1145/3673791.3698422(125-134)Online publication date: 8-Dec-2024
https://dl.acm.org/doi/10.1145/3673791.3698422
Campbell FSilberstein AStoyanovich JMoskovitch Y(2024)Query Refinement for Diverse Top-k SelectionProceedings of the ACM on Management of Data10.1145/36549692:3(1-27)Online publication date: 30-May-2024
https://dl.acm.org/doi/10.1145/3654969
Corsi MUrbano JHui Yang GWang HHan SHauff CZuccon GZhang Y(2024)The Treatment of Ties in Rank-Biased OverlapProceedings of the 47th International ACM SIGIR Conference on Research and Development in Information Retrieval10.1145/3626772.3657700(251-260)Online publication date: 10-Jul-2024
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Schimek MVitale LPfeifer BLa Rocca M(2024)Effective signal reconstruction from multiple ranked lists via convex optimizationData Mining and Knowledge Discovery10.1007/s10618-023-00991-z38:3(1125-1169)Online publication date: 1-May-2024
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Betello FSiciliano FMishra PSilvestri F(2024)Investigating the Robustness of Sequential Recommender Systems Against Training Data PerturbationsAdvances in Information Retrieval10.1007/978-3-031-56060-6_14(205-220)Online publication date: 24-Mar-2024
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Li XFan WSong SLi YLi BShao YZhan DKoyejo SMohamed SAgarwal ABelgrave DCho KOh A(2022)Asymmetric temperature scaling makes larger networks teach well againProceedings of the 36th International Conference on Neural Information Processing Systems10.5555/3600270.3600547(3830-3842)Online publication date: 28-Nov-2022
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