Two Efficient Hashing Schemes for High-Dimensional Furthest Neighbor Search

Abstract

The $c$ -Approximate Furthest Neighbor ( $c$ -AFN) search is a fundamental problem in many applications. However, existing hashing schemes for $c$ -AFN search are designed for internal memory. The old techniques for external memory, such as furthest point Voronoi diagram and the tree-based methods, are only suitable for the low-dimensional case. In this paper, we introduce a novel concept of the Reverse Locality-Sensitive Hashing (RLSH) family which is directly designed for $c$ -AFN search. Accordingly, we propose a new reverse query-aware LSH function, which is a random projection coupled with query-aware interval identification. Based on the reverse query-aware LSH functions, we introduce a novel Reverse Query-Aware LSH scheme named RQALSH for high-dimensional $c$ -AFN search over external memory. Our theoretical studies show that RQALSH enjoys a guarantee on query quality. In addition, in order to further speed up RQALSH, we propose a heuristic variant named RQALSH $^*$ which applies a data-dependent objects selection to largely reduce the number of data objects. In the experiment, we compare with two state-of-the-art hashing schemes QDAFN and DrusillaSelect which have been adapted for external memory. Extensive experiments on four real datasets show that our proposed RQALSH and RQALSH $^*$ schemes significantly outperform these two methods.