Locality sensitive hashing for set-queries, motivated by group recommendations

Haim Kaplan, Jay Tenenbaum

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Locality Sensitive Hashing (LSH) is an effective method to index a set of points such that we can efficiently find the nearest neighbors of a query point. We extend this method to our novel Set-query LSH (SLSH), such that it can find the nearest neighbors of a set of points, given as a query. Let s(x, y) be the similarity between two points x and y. We define a similarity between a set Q and a point x by aggregating the similarities s(p, x) for all p ∈ Q. For example, we can take s(p, x) to be the angular similarity between p and x (i.e., 1 − z(x,p) ), and aggregate by arithmetic π or geometric averaging, or taking the lowest similarity. We develop locality sensitive hash families and data structures for a large set of such arithmetic and geometric averaging similarities, and analyze their collision probabilities. We also establish an analogous framework and hash families for distance functions. Specifically, we give a structure for the euclidean distance aggregated by either averaging or taking the maximum. We leverage SLSH to solve a geometric extension of the approximate near neighbors problem. In this version, we consider a metric for which the unit ball is an ellipsoid and its orientation is specified with the query. An important application that motivates our work is group recommendation systems. Such a system embeds movies and users in the same feature space, and the task of recommending a movie for a group to watch together, translates to a set-query Q using an appropriate similarity.

Original languageEnglish
Title of host publication17th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2020
EditorsSusanne Albers
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771504
DOIs
StatePublished - 1 Jun 2020
Event17th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2020 - Torshavn, Faroe Islands
Duration: 22 Jun 202024 Jun 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume162
ISSN (Print)1868-8969

Conference

Conference17th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2020
Country/TerritoryFaroe Islands
CityTorshavn
Period22/06/2024/06/20

Keywords

  • Distance functions
  • Ellipsoid
  • Group recommendations
  • Locality sensitive hashing
  • Nearest neighbors
  • Similarity functions
  • Similarity search

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