License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2017.54
URN: urn:nbn:de:0030-drops-81688
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8168/
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Chierichetti, Flavio ; Kumar, Ravi ; Panconesi, Alessandro ; Terolli, Erisa

The Distortion of Locality Sensitive Hashing

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LIPIcs-ITCS-2017-54.pdf (0.7 MB)

Abstract

Given a pairwise similarity notion between objects, locality sensitive hashing (LSH) aims to construct a hash function family over the universe of objects such that the probability two objects hash to the same value is their similarity. LSH is a powerful algorithmic tool for large-scale applications and much work has been done to understand LSHable similarities, i.e., similarities that admit an LSH.
In this paper we focus on similarities that are provably non-LSHable and propose a notion of distortion to capture the approximation of such a similarity by a similarity that is LSHable. We consider several well-known non-LSHable similarities and show tight upper and lower bounds on their distortion. We also experimentally show that our upper bounds translate to e

BibTeX - Entry

@InProceedings{chierichetti_et_al:LIPIcs:2017:8168,
  author =	{Flavio Chierichetti and Ravi Kumar and Alessandro Panconesi and Erisa Terolli},
  title =	{{The Distortion of Locality Sensitive Hashing}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{54:1--54:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Christos H. Papadimitriou},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8168},
  URN =		{urn:nbn:de:0030-drops-81688},
  doi =		{10.4230/LIPIcs.ITCS.2017.54},
  annote =	{Keywords: locality sensitive hashing, distortion, similarity}
}

Keywords: locality sensitive hashing, distortion, similarity
Collection: 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)
Issue Date: 2017
Date of publication: 28.11.2017

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