Fast and exact fixed-radius neighbor search based on sorting

TL;DR

This paper introduces SNN, a fast, exact fixed-radius neighbor search method that uses data sorting and linear algebra to outperform traditional brute force and tree-based approaches without needing parameter tuning.

Contribution

The paper presents SNN, a novel fixed-radius neighbor search algorithm that is faster, exact, parameter-free, and leverages data sorting and BLAS for efficiency.

Findings

SNN significantly reduces index and query time compared to brute force and tree-based methods.

SNN provably returns exact neighbor search results.

SNN improves clustering performance when integrated with DBSCAN.

Abstract

Fixed-radius near neighbor search is a fundamental data operation that retrieves all data points within a user-specified distance to a query point. There are efficient algorithms that can provide fast approximate query responses, but they often have a very compute-intensive indexing phase and require careful parameter tuning. Therefore, exact brute force and tree-based search methods are still widely used. Here we propose a new fixed-radius near neighbor search method, called SNN, that significantly improves over brute force and tree-based methods in terms of index and query time, provably returns exact results, and requires no parameter tuning. SNN exploits a sorting of the data points by their first principal component to prune the query search space. Further speedup is gained from an efficient implementation using high-level Basic Linear Algebra Subprograms (BLAS). We provide theoretical analysis of our method and demonstrate its practical performance when used stand-alone and when applied within the DBSCAN clustering algorithm.