Generic LSH Families for the Angular Distance Based on Johnson-Lindenstrauss Projections and Feature Hashing LSH

TL;DR

This paper introduces new Locality-Sensitive Hashing (LSH) families for angular distance using Johnson-Lindenstrauss projections and feature hashing, demonstrating improved performance on synthetic and real datasets.

Contribution

It presents novel LSH families based on feature hashing and Johnson-Lindenstrauss projections, with theoretical analysis and practical validation for angular and Euclidean distances.

Findings

New LSH families outperform existing methods in experiments.

Feature hashing is validated as a Johnson-Lindenstrauss projection.

Proposed methods work effectively for both angular and Euclidean distances.

Abstract

In this paper we propose the creation of generic LSH families for the angular distance based on Johnson-Lindenstrauss projections. We show that feature hashing is a valid J-L projection and propose two new LSH families based on feature hashing. These new LSH families are tested on both synthetic and real datasets with very good results and a considerable performance improvement over other LSH families. While the theoretical analysis is done for the angular distance, these families can also be used in practice for the euclidean distance with excellent results [2]. Our tests using real datasets show that the proposed LSH functions work well for the euclidean distance.