Maximum Inner-Product Search using Tree Data-structures

TL;DR

This paper introduces new tree-based algorithms for maximum inner-product search, significantly improving search efficiency over naive methods, with up to five orders of magnitude faster performance demonstrated on diverse datasets.

Contribution

It presents the first general branch-and-bound and dual-tree algorithms for inner-product-based best match search, along with a novel data structure to enhance dual-tree efficiency.

Findings

Up to five orders of magnitude faster query times.

Effective on various datasets from multiple applications.

Novel bounds improve search efficiency.

Abstract

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.