Aren't we all nearest neighbors: Spatial trees, high dimensional reductions and batch nearest neighbor search

TL;DR

This paper reviews nearest neighbor search techniques, explores reductions between proximity problems, unifies spatial trees under a meta-tree framework, and introduces a dual tree algorithm for batch nearest neighbor search, providing insights into their complexities.

Contribution

It introduces a unified meta-tree framework for spatial partitioning trees and proposes a dual tree algorithm for efficient batch nearest neighbor search.

Findings

Reductions between nearest neighbor and other proximity problems are demonstrated.

A unified framework for spatial trees is proposed.

Complexity analysis of batch nearest neighbor search is provided.

Abstract

We start with a review of the pervasiveness of the nearest neighbor search problem and techniques used to solve it along with some experimental results. In the second chapter, we show reductions between two different classes of geo- metric proximity problems: the nearest neighbor problems to solve the Euclidean minimum spanning tree problem and the farthest neighbor problems to solve the k-centers problem. In the third chapter, we unify spatial partitioning trees un- der one framework the meta-tree. Finally, we propose a dual tree algorithm for Bichromatic Closest Pair and measure the complexity of batch nearest neighbor search.