The Voronoi Density Estimator (VDE) is an established density estimation technique that adapts to the local geometry of data. However, its applicability has been so far limited to problems in two and three dimensions. This is because Voronoi cells rapidly increase in complexity as dimensions grow, making the necessary explicit computations infeasible. We define a variant of the VDE deemed Compactified Voronoi Density Estimator (CVDE), suitable for higher dimensions. We propose computationally efficient algorithms for numerical approximation of the CVDE and formally prove convergence of the estimated density to the original one. We implement and empirically validate the CVDE through a comparison with the Kernel Density Estimator (KDE). Our results indicate that the CVDE outperforms the KDE on sound and image data.

翻译：Voroni密度估计器（VDE）是一种成熟的密度估计技术，能够自适应数据的局部几何结构。然而，其应用至今仍局限于二维和三维问题，这是因为随着维度增长，Voronoi单元的复杂度迅速增加，导致必要的显式计算不可行。我们定义了一种适用于更高维度的VDE变体——紧凑化Voronoi密度估计器（CVDE），并提出了用于CVDE数值逼近的高效计算算法，从数学上证明了估计密度向原始密度的收敛性。通过实现CVDE并与核密度估计器（KDE）进行实证对比，结果表明CVDE在声音和图像数据上的性能优于KDE。