Quantitative Comparison of Nearest Neighbor Search Algorithms

TL;DR

This paper provides a comprehensive quantitative comparison of three popular nearest neighbor search algorithms—Orchard, ball tree, and VP-tree—analyzing their efficiency relative to dataset size and dimension to guide optimal algorithm selection.

Contribution

It introduces derived fitting functions for each algorithm's efficiency based on dataset size and dimension, offering new insights into their performance characteristics.

Findings

Ball tree and VP-tree outperform Orchard in high-dimensional spaces.

Efficiency varies significantly with dataset size and dimension.

The derived functions accurately predict algorithm performance.

Abstract

We compare the performance of three nearest neighbor search algorithms: the Orchard, ball tree, and VP-tree algorithms. These algorithms are commonly used for nearest-neighbor searches and are known for their efficiency in large datasets. We analyze the fraction of distances computed in relation to the size of the dataset and its dimension. For each algorithm we derive a fitting function for the efficiency as a function to set size and dimension. The article aims to provide a comprehensive analysis of the performance of these algorithms and help researchers and practitioners choose the best algorithm for their specific application.