A Sub-linear Time Algorithm for Approximating k-Nearest-Neighbor with Full Quality Guarantee

TL;DR

This paper introduces a novel algorithm for approximate k-Nearest-Neighbors that unifies distance and recall criteria with full theoretical guarantees, achieving sub-linear query time, a first in the field.

Contribution

It presents the first algorithm to combine sub-linear query time with full theoretical approximation guarantees for k-NN.

Findings

Achieves sub-linear query time for k-NN approximation.

Provides full theoretical guarantees for both distance and recall criteria.

Unifies two approximation criteria in a single algorithm.

Abstract

In this paper we propose an algorithm for the approximate k-Nearest-Neighbors problem. According to the existing researches, there are two kinds of approximation criterion. One is the distance criteria, and the other is the recall criteria. All former algorithms suffer the problem that there are no theoretical guarantees for the two approximation criterion. The algorithm proposed in this paper unifies the two kinds of approximation criterion, and has full theoretical guarantees. Furthermore, the query time of the algorithm is sub-linear. As far as we know, it is the first algorithm that achieves both sub-linear query time and full theoretical approximation guarantee.