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：我们提出了一种名为径向Voronoi密度估计器（RVDE）的非参数密度估计方法。RVDE基于Voronoi剖分的几何特性，因此具有局部几何自适应性和广泛的收敛性质。由于其径向定义，RVDE是连续的，且计算复杂度与数据集规模成线性关系。这弥补了此前研究的VDE的主要缺陷——高度不连续且计算成本高昂。我们从理论上研究了RVDE的模态，并在高维数据上对其性能进行了实验性评估。结果表明，RVDE优于其他非参数密度估计方法，包括近期提出的VDE。