Reverse Maximum Inner Product Search: Formulation, Algorithms, and Analysis

The maximum inner product search (MIPS), which finds the item with highest a given query user, is an essential problem in recommendation field. Usually e-commerce companies face situations where they want to promote and sell new or discounted items. In these situations, we have consider following questions: Who interested items, how do find them? This article answers this question by addressing called reverse (reverse MIPS). Given vector two sets of vectors (user vectors), MIPS set user whose among vectors. Although importance clear, its straightforward implementation incurs computationally expensive cost. We therefore propose Simpfer, simple, fast, exact algorithm for MIPS. offline phase, Simpfer builds simple index that maintains lower bound product. By exploiting index, judges whether can not, vector, constant time. Our enables filtering vectors, cannot batch. theoretically demonstrate outperforms baselines employing state-of-the-art techniques. addition, answer research questions. Can approximation algorithms further improve processing? Is there faster than Simpfer? For former, show quality guarantee provides little speed-up. latter, Simpfer++, practically Simpfer. extensive experiments on real datasets at least orders magnitude baselines, Simpfer++ improves online processing