{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/sah-shifting-aware-asymmetric-hashing-for","title":"SAH: Shifting-aware Asymmetric Hashing for Reverse $k$-Maximum Inner Product Search","arxiv_id":"2211.12751","date":"2022-11-23","proceeding":null,"authors":["Qiang Huang","Yanhao Wang","Anthony K. H. Tung"],"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}.","url_abs":"https://arxiv.org/abs/2211.12751v1","url_pdf":"https://arxiv.org/pdf/2211.12751v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"sah-shifting-aware-asymmetric-hashing-for","repo_url":"https://github.com/huangqiang/sah","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"blocking","task_name":"Blocking"}],"methods":[{"method_slug":"speed","method_name":"SPEED"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2211.12751","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}