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

TL;DR

This paper introduces SAH, a novel subquadratic algorithm for Reverse k-Maximum Inner Product Search, combining shifting-invariant transformations and a cone-tree based pruning strategy to significantly improve speed and accuracy.

Contribution

The paper proposes the first subquadratic-time algorithm for RkMIPS, integrating a shifting-invariant transformation, a new hashing scheme, and a cone-tree based pruning method.

Findings

SAH is 4-8 times faster than existing methods.

SAH achieves over 90% F1-score on real datasets.

Theoretical guarantees support the effectiveness of SAH.

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}.