论文标题
高维数据的Voronoi密度估计器：计算，紧凑和收敛
Voronoi Density Estimator for High-Dimensional Data: Computation, Compactification and Convergence
论文作者
论文摘要
Voronoi密度估计量（VDE）是一种已建立的密度估计技术，可适应数据的局部几何形状。但是，到目前为止，其适用性仅限于两个维度和三个维度的问题。这是因为随着尺寸的增长，Voronoi细胞的复杂性迅速增加，这使得必要的明确计算不可行。我们定义了VDE被认为是压缩的Voronoi密度估计器（CVDE）的变体，适用于更高的尺寸。我们提出了用于CVDE的数值近似值的计算有效算法，并正式证明了估计密度与原始密度的收敛性。我们通过与内核密度估计器（KDE）进行比较来实施并验证CVDE。我们的结果表明，CVDE在声音和图像数据上的表现优于KDE。
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.
