Optimal Load Factor for Approximate Nearest Neighbor Search under Exact Euclidean Locality Sensitive Hashing

Abstract

Locality Sensitive Hashing (LSH) is an index-based data structure that allows spatial item retrieval over a large dataset. The performance measure, ρ, has significant effect on the computational complexity and memory space requirement to create and store items in this data structure respectively. The minimization of ρ at a specific approximation factor c, is dependent on the load factor, α. Over the years,α = 4has been used by researchers. In this paper, we demonstratethat the choice ofα = 4does not guarantee low computational complexity and low memory space of the data structure under the LSH scheme. To guarantee low computational complexity and low memory space, we proposeα = 5. Experiments on the Defense Meteorological Satellite Program imagery datasethave shown thatα = 5saves more than 75%on memory space; cuts the computational complexity by more than 70%andanswers query two times faster on the average compared to that ofα = 4. General Terms Nearest Neighbor, Search Algorithm, Locality Sensitive Hashing