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

IF 2.6 4区 计算机科学 Q2 COMPUTER SCIENCE, INFORMATION SYSTEMS ACM Transactions on the Web Pub Date : 2023-07-11 DOI:https://dl.acm.org/doi/10.1145/3587215
Daichi Amagata, Takahiro Hara
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Abstract

The maximum inner product search (MIPS), which finds the item with the highest inner product with a given query user, is an essential problem in the recommendation field. Usually e-commerce companies face situations where they want to promote and sell new or discounted items. In these situations, we have to consider the following questions: Who is interested in the items, and how do we find them? This article answers this question by addressing a new problem called reverse maximum inner product search (reverse MIPS). Given a query vector and two sets of vectors (user vectors and item vectors), the problem of reverse MIPS finds a set of user vectors whose inner product with the query vector is the maximum among the query and item vectors. Although the importance of this problem is clear, its straightforward implementation incurs a computationally expensive cost.

We therefore propose Simpfer, a simple, fast, and exact algorithm for reverse MIPS. In an offline phase, Simpfer builds a simple index that maintains a lower bound of the maximum inner product. By exploiting this index, Simpfer judges whether the query vector can have the maximum inner product or not, for a given user vector, in a constant time. Our index enables filtering user vectors, which cannot have the maximum inner product with the query vector, in a batch. We theoretically demonstrate that Simpfer outperforms baselines employing state-of-the-art MIPS techniques. In addition, we answer two new research questions. Can approximation algorithms further improve reverse MIPS processing? Is there an exact algorithm that is faster than Simpfer? For the former, we show that approximation with quality guarantee provides a little speed-up. For the latter, we propose Simpfer++, a theoretically and practically faster algorithm than Simpfer. Our extensive experiments on real datasets show that Simpfer is at least two orders of magnitude faster than the baselines, and Simpfer++ further improves the online processing time.

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反向最大内积搜索:公式、算法和分析
最大内积搜索(MIPS)是推荐领域的一个重要问题,即在给定的查询用户中找到具有最大内积的商品。通常电子商务公司面临的情况是,他们想要推广和销售新的或打折的商品。在这些情况下,我们必须考虑以下问题:谁对这些物品感兴趣,我们如何找到它们?本文通过解决一个称为反向最大内积搜索(reverse MIPS)的新问题来回答这个问题。给定一个查询向量和两组向量(用户向量和项目向量),反向MIPS问题在查询向量和项目向量中找到一组与查询向量内积最大的用户向量。虽然这个问题的重要性是显而易见的,但它的直接实现会导致计算成本高昂。因此,我们提出了一种简单、快速、精确的反向MIPS算法。在脱机阶段,Simpfer构建一个简单索引,该索引维护最大内积的下界。通过利用这个索引,Simpfer判断查询向量在一定时间内对于给定的用户向量是否具有最大内积。我们的索引可以过滤用户向量,这些用户向量不能与查询向量有最大的内积。我们从理论上证明Simpfer优于采用最先进的MIPS技术的基线。此外,我们还回答了两个新的研究问题。近似算法能进一步改善反向MIPS处理吗?有没有比simplfer更快的精确算法?对于前者,我们证明了带质量保证的近似能提供少量的加速。对于后者,我们提出了Simpfer++,这是一种理论和实践上都比Simpfer更快的算法。我们在真实数据集上的大量实验表明,Simpfer比基线至少快两个数量级,并且Simpfer++进一步提高了在线处理时间。
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来源期刊
ACM Transactions on the Web
ACM Transactions on the Web 工程技术-计算机:软件工程
CiteScore
4.90
自引率
0.00%
发文量
26
审稿时长
7.5 months
期刊介绍: Transactions on the Web (TWEB) is a journal publishing refereed articles reporting the results of research on Web content, applications, use, and related enabling technologies. Topics in the scope of TWEB include but are not limited to the following: Browsers and Web Interfaces; Electronic Commerce; Electronic Publishing; Hypertext and Hypermedia; Semantic Web; Web Engineering; Web Services; and Service-Oriented Computing XML. In addition, papers addressing the intersection of the following broader technologies with the Web are also in scope: Accessibility; Business Services Education; Knowledge Management and Representation; Mobility and pervasive computing; Performance and scalability; Recommender systems; Searching, Indexing, Classification, Retrieval and Querying, Data Mining and Analysis; Security and Privacy; and User Interfaces. Papers discussing specific Web technologies, applications, content generation and management and use are within scope. Also, papers describing novel applications of the web as well as papers on the underlying technologies are welcome.
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