基于树数据结构的最大内积搜索
Maximum Inner-Product Search using Tree Data-structures
摘要：
文献中广泛研究了{ \em efficiently}在给定集合中关于欧氏距离或余弦相似度为查询找到最佳匹配的问题。然而，一个密切相关的问题，有效地找到最佳匹配的内积从来没有探索在一般设置，以我们的知识。在本文中，我们考虑这个一般性的问题，并将其与现有的最佳匹配算法进行对比。首先，我们提出了一个通用的分支定界算法使用树数据结构。随后，我们提出了一个双树算法的情况下，有多个查询。最后，我们提出了一种新的数据结构，以提高双树算法的效率。这些分支定界算法涉及新的边界适合与内积最佳匹配的目的。我们评估我们提出的算法对各种应用程序的各种数据集，并表现出高达五个数量级的改善，在查询时间的天真的搜索技术。
英文摘要：
The problem of {\em efficiently} finding the best match for a query in a given set with respect to the Euclidean distance or the cosine similarity has been extensively studied in literature. However, a closely related problem of efficiently finding the best match with respect to the inner product has never been explored in the general setting to the best of our knowledge. In this paper we consider this general problem and contrast it with the existing best-match algorithms. First, we propose a general branch-and-bound algorithm using a tree data structure. Subsequently, we present a dual-tree algorithm for the case where there are multiple queries. Finally we present a new data structure for increasing the efficiency of the dual-tree algorithm. These branch-and-bound algorithms involve novel bounds suited for the purpose of best-matching with inner products. We evaluate our proposed algorithms on a variety of data sets from various applications, and exhibit up to five orders of magnitude improvement in query time over the naive search technique.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
