2026-08-12T09:19:09Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:12275 2024-03-06T10:49:30Z ddc:004 open_access

Locality Sensitive Hashing for Set-Queries, Motivated by Group Recommendations Kaplan, Haim Tenenbaum, Jay Locality sensitive hashing nearest neighbors similarity search group recommendations distance functions similarity functions ellipsoid 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-(∠(x,p)/π)), and aggregate by arithmetic 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Haim Kaplan and Jay Tenenbaum 2020 Is Part Of LIPIcs, Volume 162, 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SWAT.2020.28 urn:nbn:de:0030-drops-122756 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2020.28 eng https://creativecommons.org/licenses/by/3.0/legalcode