一种基于高斯核的广义数据深度  

A General Data Depth Function Based on Gaussian Kernel

作　　者：胡永刚[1] 吴翊[1] 李强[1] 

机构地区：[1]国防科技大学数学与系统科学系,长沙410073

出　　处：《应用数学学报》2009年第4期746-756,共11页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(60673090)资助项目

摘　　要：本文提出了一个具有自适应等深面的广义数据深度函数。针对目前数据深度函数的中心区域都是凸的,造成无法有效处理具有凹形结构数据的问题。本文从样本深度的角度,利用高斯核特征空间最小球原理,提出了一种广义的数据深度。它具有正交、尺度、平移不变性,满足弱单调性和无穷远处为0的性质。相比现有数据深度而言,它对凹形结构的数据具有更好的深度解释。更为重要的是它的计算比较简单,从而保证了它的实用性。This paper presents a general data depth function with adaptive shape of deep contours based on Gaussian kernel function. Since the contours of almost all depth functions are convex, they cannot reasonably interpret the data sets with concave shape. Thus, we propose a new depth function to deal with such concave shape data sets using the principal of smallest hypersphere in the Gaussian kernel feature space. The Gaussian kernel depth function is orthogonal transformation, scale and displace invariant, and it also satisfies weak monotonicity and vanishing at infinity. Furthermore, it not only has better interpretability to the concave data sets than the existing depth functions, but also has a relative simple computation, which ensures its practicality.

关 键 词：数据深度 高斯核 凸形数据 凹形数据 统计深度 

分 类 号：O212[理学—概率论与数理统计]