Illumination Depth
利用凸几何中的照明体概念改进多元数据的半空间深度，能更精细地区分样本点、打破深度排序中的平局，并为凸包外的点定义深度函数，具有仿射不变、稳健、一致收敛等优良性质。
The concept of illumination bodies studied in convex geometry is used to amend the halfspace depth for multivariate data. The proposed notion of illumination enables finer resolution of the sample points, naturally breaks ties in the associated depth-based ordering, and introduces a depth-like function for points outside the convex hull of the support of the probability measure. The illumination is, in a certain sense, dual to the halfspace depth mapping, and shares the majority of its beneficial properties. It is affine invariant, robust, uniformly consistent, and aligns well with common probability distributions. Supplementary materials for this article are available online.