Fast and exact fixed-radius neighbor search based on sorting
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866914656707149824 |
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| author | Chen, Xinye Güttel, Stefan |
| author_facet | Chen, Xinye Güttel, Stefan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_07679 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Fast and exact fixed-radius neighbor search based on sorting Chen, Xinye Güttel, Stefan Information Retrieval Data Structures and Algorithms 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. |
| title | Fast and exact fixed-radius neighbor search based on sorting |
| topic | Information Retrieval Data Structures and Algorithms |
| url | https://arxiv.org/abs/2212.07679 |