Article

Similarity estimation techniques from rounding algorithms

Author:

Moses S. CharikarAuthors Info & Claims

STOC '02: Proceedings of the thiry-fourth annual ACM symposium on Theory of computing

Pages 380 - 388

https://doi.org/10.1145/509907.509965

Published: 19 May 2002 Publication History

Abstract

(MATH) A locality sensitive hashing scheme is a distribution on a family $\F$ of hash functions operating on a collection of objects, such that for two objects x,y, Pr_hεF[h(x) = h(y)] = sim(x,y), where sim(x,y) ε [0,1] is some similarity function defined on the collection of objects. Such a scheme leads to a compact representation of objects so that similarity of objects can be estimated from their compact sketches, and also leads to efficient algorithms for approximate nearest neighbor search and clustering. Min-wise independent permutations provide an elegant construction of such a locality sensitive hashing scheme for a collection of subsets with the set similarity measure sim(A,B) = \frac{|A ∩ B|}{|A ∪ B|}.(MATH) We show that rounding algorithms for LPs and SDPs used in the context of approximation algorithms can be viewed as locality sensitive hashing schemes for several interesting collections of objects. Based on this insight, we construct new locality sensitive hashing schemes for:

A collection of vectors with the distance between → \over u and → \over v measured by Ø(→ \over u, → \over v)/π, where Ø(→ \over u, → \over v) is the angle between → \over u) and → \over v). This yields a sketching scheme for estimating the cosine similarity measure between two vectors, as well as a simple alternative to minwise independent permutations for estimating set similarity.

A collection of distributions on n points in a metric space, with distance between distributions measured by the Earth Mover Distance (EMD), (a popular distance measure in graphics and vision). Our hash functions map distributions to points in the metric space such that, for distributions P and Q, EMD(P,Q) ≤ E_hε\F [d(h(P),h(Q))] ≤ O(log n log log n). EMD(P, Q).

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Similarity estimation techniques from rounding algorithms

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cover image ACM Conferences

STOC '02: Proceedings of the thiry-fourth annual ACM symposium on Theory of computing

May 2002

840 pages

ISBN:1581134959

DOI:10.1145/509907

Conference Chair:
John Reif
Duke University

Copyright © 2002 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

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Published: 19 May 2002

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STOC02: Symposium on the Theory of Computing

May 19 - 21, 2002

Quebec, Montreal, Canada

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STOC '02 Paper Acceptance Rate 91 of 287 submissions, 32%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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