{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/lightweight-yet-efficient-revitalizing-ball","title":"Lightweight-Yet-Efficient: Revitalizing Ball-Tree for Point-to-Hyperplane Nearest Neighbor Search","arxiv_id":"2302.10626","date":"2023-02-21","proceeding":null,"authors":["Qiang Huang","Anthony K. H. Tung"],"abstract":"Finding the nearest neighbor to a hyperplane (or Point-to-Hyperplane Nearest Neighbor Search, simply P2HNNS) is a new and challenging problem with applications in many research domains. While existing state-of-the-art hashing schemes (e.g., NH and FH) are able to achieve sublinear time complexity without the assumption of the data being in a unit hypersphere, they require an asymmetric transformation, which increases the data dimension from $d$ to $\\Omega(d^2)$. This leads to considerable overhead for indexing and incurs significant distortion errors. In this paper, we investigate a tree-based approach for solving P2HNNS using the classical Ball-Tree index. Compared to hashing-based methods, tree-based methods usually require roughly linear costs for construction, and they provide different kinds of approximations with excellent flexibility. A simple branch-and-bound algorithm with a novel lower bound is first developed on Ball-Tree for performing P2HNNS. Then, a new tree structure named BC-Tree, which maintains the Ball and Cone structures in the leaf nodes of Ball-Tree, is described together with two effective strategies, i.e., point-level pruning and collaborative inner product computing. BC-Tree inherits both the low construction cost and lightweight property of Ball-Tree while providing a similar or more efficient search. Experimental results over 16 real-world data sets show that Ball-Tree and BC-Tree are around 1.1$\\sim$10$\\times$ faster than NH and FH, and they can reduce the index size and indexing time by about 1$\\sim$3 orders of magnitudes on average. The code is available at \\url{https://github.com/HuangQiang/BC-Tree}.","url_abs":"https://arxiv.org/abs/2302.10626v1","url_pdf":"https://arxiv.org/pdf/2302.10626v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"lightweight-yet-efficient-revitalizing-ball","repo_url":"https://github.com/huangqiang/bc-tree","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[{"method_slug":"pruning","method_name":"Pruning"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}