Spherical LSH for Approximate Nearest Neighbor Search on Unit Hypersphere

Abstract

LSH (Locality Sensitive Hashing) is one of the best known methods for solving the c-approximate nearest neighbor problem in high dimensional spaces. This paper presents a variant of the LSH algorithm, focusing on the special case of where all points in the dataset lie on the surface of the unit hypersphere in a d-dimensional Euclidean space. The LSH scheme is based on a family of hash functions that preserves locality of points. This paper points out that when all points are constrained to lie on the surface of the unit hypersphere, there exist hash functions that partition the space more efficiently than the previously proposed methods. The design of these hash functions uses randomly rotated regular polytopes and it partitions the surface of the unit hypersphere like a Voronoi diagram. Our new scheme improves the exponent ρ, the main indicator of the performance of the LSH algorithm.