Fast Locality Sensitive Hashing with Theoretical Guarantee

TL;DR

FastLSH is an efficient LSH scheme for high-dimensional data that reduces computation time significantly while maintaining comparable accuracy, making it a promising alternative to traditional methods.

Contribution

The paper introduces FastLSH, a novel LSH scheme combining sampling and projection to improve efficiency with provable guarantees.

Findings

FastLSH reduces hash computation from O(n) to O(m) time.

FastLSH achieves up to 80x speedup in hash evaluation.

FastLSH maintains comparable accuracy and space efficiency to state-of-the-art methods.

Abstract

Locality-sensitive hashing (LSH) is an effective randomized technique widely used in many machine learning tasks. The cost of hashing is proportional to data dimensions, and thus often the performance bottleneck when dimensionality is high and the number of hash functions involved is large. Surprisingly, however, little work has been done to improve the efficiency of LSH computation. In this paper, we design a simple yet efficient LSH scheme, named FastLSH, under l2 norm. By combining random sampling and random projection, FastLSH reduces the time complexity from O(n) to O(m) (m<n), where n is the data dimensionality and m is the number of sampled dimensions. Moreover, FastLSH has provable LSH property, which distinguishes it from the non-LSH fast sketches. We conduct comprehensive experiments over a collection of real and synthetic datasets for the nearest neighbor search task. Experimental results demonstrate that FastLSH is on par with the state-of-the-arts in terms of answer quality, space occupation and query efficiency, while enjoying up to 80x speedup in hash function evaluation. We believe that FastLSH is a promising alternative to the classic LSH scheme.