一种完全数据驱动的点云形状估计方法
A fully data-driven method for estimating the shape of a point cloud
摘要：
给定一个未知分布的随机样本点，我们提出了一个新的数据驱动的方法来估计其概率支持度$S$。在$S$是$r$ -凸的温和假设下，包含样本点的最小$r$ -凸集是自然估计。在实践中使用该估计器的主要问题是$r$是集合$S$的未知几何特征。在样本均匀产生的假设下，提出了一种从数据中选择它的随机算法。新的数据驱动的重建$S$是能够实现相同的收敛速度的凸包估计凸集，但在一个更灵活的光滑形状条件。通过一个实际数据的例子和模拟研究的估计器的实际性能说明。
英文摘要：
Given a random sample of points from some unknown distribution, we propose a new data-driven method for estimating its probability support $S$. Under the mild assumption that $S$ is $r$-convex, the smallest $r$-convex set which contains the sample points is the natural estimator. The main problem for using this estimator in practice is that $r$ is an unknown geometric characteristic of the set $S$. A stochastic algorithm is proposed for selecting it from the data under the hypothesis that the sample is uniformly generated. The new data-driven reconstruction of $S$ is able to achieve the same convergence rates as the convex hull for estimating convex sets, but under a much more flexible smoothness shape condition. The practical performance of the estimator is illustrated through a real data example and a simulation study.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
