Introduction to Modern Information Retrieval
Introduction to Modern Information Retrieval
Similarity Search in High Dimensions via Hashing
VLDB '99 Proceedings of the 25th International Conference on Very Large Data Bases
Object Recognition from Local Scale-Invariant Features
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
A Replacement for Voronoi Diagrams of Near Linear Size
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Distinctive Image Features from Scale-Invariant Keypoints
International Journal of Computer Vision
Locality-sensitive hashing scheme based on p-stable distributions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Near-Optimal Hashing Algorithms for Approximate Nearest Neighbor in High Dimensions
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions
Communications of the ACM - 50th anniversary issue: 1958 - 2008
Optimal Lower Bounds for Locality-Sensitive Hashing (Except When q is Tiny)
ACM Transactions on Computation Theory (TOCT)
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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.