Spatial depth for data in metric spaces
提出一种适用于任意度量空间的统计深度指标，用于衡量数据点的中心性或异常程度，在欧氏空间中退化为经典空间深度，并在异常检测、非凸深度区域估计和分类中展示实用性。
Abstract We propose a novel measure of statistical depth, the metric spatial depth, for data residing in an arbitrary metric space. The measure assigns high (low) values for points located near (far away from) the bulk of the data distribution, allowing quantifying their centrality/outlyingness. This depth measure is shown to have highly interpretable properties, making it appealing in object data analysis where standard descriptive statistics are difficult to compute. The proposed measure reduces to the classical spatial depth in a Euclidean space. In addition to studying its theoretical properties, to provide intuition on the concept, we explicitly compute metric spatial depths in several different metric spaces. Finally, we showcase the practical usefulness of the metric spatial depth in outlier detection, non‐convex depth region estimation and classification.