Generic LSH Families for the Angular Distance Based on Johnson-Lindenstrauss Projections and Feature Hashing LSH
This work addresses the need for efficient similarity search in high-dimensional data, offering incremental improvements in LSH techniques for angular and Euclidean distances.
The paper tackles the problem of creating generic Locality-Sensitive Hashing (LSH) families for angular distance by using Johnson-Lindenstrauss projections and feature hashing, resulting in two new LSH families that show very good results and considerable performance improvement over existing methods on synthetic and real datasets.
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.