A Framework for Similarity Search with Space-Time Tradeoffs using Locality-Sensitive Filtering
Tobias Christiani

TL;DR
This paper introduces a generalized framework for similarity search using Locality-Sensitive Filtering, enabling flexible space-time tradeoffs and improving upon previous methods for high-dimensional data, with theoretical bounds and practical implications.
Contribution
It extends the LSF framework to support adjustable space-time tradeoffs without relying on an oracle, and applies kernel embedding techniques to improve near neighbor search in high-dimensional spaces.
Findings
Achieves space-time tradeoffs with query time $dn^{ ho_q+o(1)}$ and update time $dn^{ ho_u+o(1)}$
Provides improved exponents for near neighbor search in $ ext{l}_s^d$-space
Establishes matching lower bounds for the space-time tradeoff on the unit sphere
Abstract
We present a framework for similarity search based on Locality-Sensitive Filtering (LSF), generalizing the Indyk-Motwani (STOC 1998) Locality-Sensitive Hashing (LSH) framework to support space-time tradeoffs. Given a family of filters, defined as a distribution over pairs of subsets of space with certain locality-sensitivity properties, we can solve the approximate near neighbor problem in -dimensional space for an -point data set with query time , update time , and space usage . The space-time tradeoff is tied to the tradeoff between query time and update time, controlled by the exponents that are determined by the filter family. Locality-sensitive filtering was introduced by Becker et al. (SODA 2016) together with a framework yielding a single, balanced, tradeoff between query time and space,…
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Taxonomy
TopicsAdvanced Image and Video Retrieval Techniques · Robotics and Sensor-Based Localization · Image Retrieval and Classification Techniques
