JBLD均值的影响函数及鲁棒性分析
Influence Function and Robustness Analysis of JBLD Mean Value
摘要: 影响函数描述了正定矩阵流形上的数据被异常值污染时，异常值对平均值估计精度的影响。本文给出了Jensen-Bregman LogDet (JBLD)均值矩阵的影响函数及鲁棒性分析。首先概述正定矩阵流形的几何结构，包括欧氏度量和JBLD度量及它们的测地距离和均值矩阵，进而计算JBLD均值的影响函数，并分析均值的稳定性。
Abstract: The influence function describes the influence of outliers on the estimation accuracy of the mean value when the data on the positive definite matrix manifold is contaminated by outliers. In this paper, the influence function of Jensen-Bregman LogDet (JBLD) mean matrix is given and its robustness is analyzed. Firstly, the geometric structure of positive definite matrix manifold is summarized, including Euclidean metric and JBLD metric, their geodesic distance and mean matrix, and then the influence function of JBLD mean is calculated, and the stability of mean is analyzed.
文章引用：冯莉. JBLD均值的影响函数及鲁棒性分析[J]. 应用数学进展, 2024, 13(8): 3694-3701. https://doi.org/10.12677/aam.2024.138352

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