Query-aware locality-sensitive hashing scheme for $$l_p$$ norm

Abstract

The problem of c-Approximate Nearest Neighbor (c-ANN) search in high-dimensional space is fundamentally important in many applications, such as image database and data mining. Locality-Sensitive Hashing (LSH) and its variants are the well-known indexing schemes to tackle the c-ANN search problem. Traditionally, LSH functions are constructed in a query-oblivious manner, in the sense that buckets are partitioned before any query arrives. However, objects closer to a query may be partitioned into different buckets, which is undesirable. Due to the use of query-oblivious bucket partition, the state-of-the-art LSH schemes for external memory, namely C2LSH and LSB-Forest, only work with approximation ratio of integer $$c \ge 2$$cź2. In this paper, we introduce a novel concept of query-aware bucket partition which uses a given query as the "anchor" for bucket partition. Accordingly, a query-aware LSH function under a specific $$l_p$$lp norm with $$p \in (0,2]$$pź(0,2] is a random projection coupled with query-aware bucket partition, which removes random shift required by traditional query-oblivious LSH functions. The query-aware bucket partitioning strategy can be easily implemented so that query performance is guaranteed. For each $$l_p$$lp norm $$(p \in (0,2])$$(pź(0,2]), based on the corresponding p-stable distribution, we propose a novel LSH scheme named query-aware LSH (QALSH) for c-ANN search over external memory. Our theoretical studies show that QALSH enjoys a guarantee on query quality. The use of query-aware LSH function enables QALSH to work with any approximation ratio $$c > 1$$c>1. In addition, we propose a heuristic variant named QALSH$$^+$$+ to improve the scalability of QALSH. Extensive experiments show that QALSH and QALSH$$^+$$+ outperform the state-of-the-art schemes, especially in high-dimensional space. Specifically, by using a ratio $$c < 2$$c<2, QALSH can achieve much better query quality.