SAH Shifting-aware Asymmetric Hashing For Reverse k-maximum Inner Product Search

Huang Qiang, Wang Yanhao, Tung Anthony K. H.. Arxiv 2022

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This paper investigates a new yet challenging problem called Reverse \(k\)-Maximum Inner Product Search (R\(k\)MIPS). Given a query (item) vector, a set of item vectors, and a set of user vectors, the problem of R\(k\)MIPS aims to find a set of user vectors whose inner products with the query vector are one of the \(k\) largest among the query and item vectors. We propose the first subquadratic-time algorithm, i.e., Shifting-aware Asymmetric Hashing (SAH), to tackle the R\(k\)MIPS problem. To speed up the Maximum Inner Product Search (MIPS) on item vectors, we design a shifting-invariant asymmetric transformation and develop a novel sublinear-time Shifting-Aware Asymmetric Locality Sensitive Hashing (SA-ALSH) scheme. Furthermore, we devise a new blocking strategy based on the Cone-Tree to effectively prune user vectors (in a batch). We prove that SAH achieves a theoretical guarantee for solving the RMIPS problem. Experimental results on five real-world datasets show that SAH runs 4\(\sim\)8\(\times\) faster than the state-of-the-art methods for R\(k\)MIPS while achieving F1-scores of over 90\%. The code is available at \url{https://github.com/HuangQiang/SAH}.

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