SAH: Shifting-aware Asymmetric Hashing for Reverse $k$-Maximum Inner Product Search

Abstract

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}.

Accepted by AAAI 2023

References in corpus (8)

• Asymmetric LSH (ALSH) for Sublinear Time Maximum Inner Product Search (MIPS)
• On Symmetric and Asymmetric LSHs for Inner Product Search
• Improved Asymmetric Locality Sensitive Hashing (ALSH) for Maximum Inner Product Search (MIPS)
• A Greedy Approach for Budgeted Maximum Inner Product Search
• Norm-Explicit Quantization: Improving Vector Quantization for Maximum Inner Product Search
• SAH: Shifting-aware Asymmetric Hashing for Reverse $k$-Maximum Inner Product Search
• Reverse Nearest Neighbors Search in High Dimensions using Locality-Sensitive Hashing
• Locality-Sensitive Hashing Scheme based on Longest Circular Co-Substring

Cited by in corpus (1)

• SAH: Shifting-aware Asymmetric Hashing for Reverse $k$-Maximum Inner Product Search