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The Distortion of Locality Sensitive Hashing

Authors Flavio Chierichetti, Ravi Kumar, Alessandro Panconesi, Erisa Terolli



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Flavio Chierichetti
Ravi Kumar
Alessandro Panconesi
Erisa Terolli

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Flavio Chierichetti, Ravi Kumar, Alessandro Panconesi, and Erisa Terolli. The Distortion of Locality Sensitive Hashing. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 54:1-54:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.ITCS.2017.54

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
Keywords
  • locality sensitive hashing
  • distortion
  • similarity

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