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Statistics > Methodology

arXiv:2210.03964 (stat)
[Submitted on 8 Oct 2022 (v1), last revised 7 Feb 2023 (this version, v2)]

Title:An Efficient and Continuous Voronoi Density Estimator

Authors:Giovanni Luca Marchetti, Vladislav Polianskii, Anastasiia Varava, Florian T. Pokorny, Danica Kragic
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Abstract:We introduce a non-parametric density estimator deemed Radial Voronoi Density Estimator (RVDE). RVDE is grounded in the geometry of Voronoi tessellations and as such benefits from local geometric adaptiveness and broad convergence properties. Due to its radial definition RVDE is continuous and computable in linear time with respect to the dataset size. This amends for the main shortcomings of previously studied VDEs, which are highly discontinuous and computationally expensive. We provide a theoretical study of the modes of RVDE as well as an empirical investigation of its performance on high-dimensional data. Results show that RVDE outperforms other non-parametric density estimators, including recently introduced VDEs.
Comments: 13 pages
Subjects: Methodology (stat.ME); Computational Geometry (cs.CG)
Cite as: arXiv:2210.03964 [stat.ME]
  (or arXiv:2210.03964v2 [stat.ME] for this version)
  https://doi.org/10.48550/arXiv.2210.03964

Submission history

From: Giovanni Luca Marchetti [view email]
[v1] Sat, 8 Oct 2022 08:13:43 UTC (2,189 KB)
[v2] Tue, 7 Feb 2023 12:34:12 UTC (2,622 KB)
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