  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.
