An Efficient and Continuous Voronoi Density Estimator
For practitioners needing fast, continuous density estimation on high-dimensional data, RVDE offers a practical improvement over existing Voronoi density estimators.
The paper introduces the Radial Voronoi Density Estimator (RVDE), a non-parametric density estimator that is continuous and computable in linear time, overcoming the discontinuity and computational expense of previous Voronoi-based estimators. RVDE outperforms other non-parametric density estimators on high-dimensional data.
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.