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.

翻译：我们引入了一种非参数密度估计值,认为其密度值为Radiarial Voronoi 密度测算器(RVDE),RVDE以Voronoi 星系的几何测量法为基础,并因此受益于当地几何适应性和广泛的趋同性。由于它的射线定义,RVDE是连续的,在线性时间内可与数据集大小进行计算。这纠正了以前研究过的VDE的主要缺点,这些缺点高度不连续,而且计算成本很高。我们提供了RVDE模式的理论研究,以及对其高维数据性能的实证调查。结果显示,RVDE优于其他非参数密度测算器,包括最近推出的VDE。