论文标题
通过Bregman总差异及其稳健性分析，向中位信号检测器朝向中位数检测器
Towards a median signal detector through the total Bregman divergence and its robustness analysis
论文作者
论文摘要
通过总Bregman Divergence（TBD）的中位数提出了一种新型的几何信号探测器，该家族在传统方法及其平均值方面的有利作用。通过将观察数据解释为遗传学阳性矩阵，它们的平均值或中位数在信号检测中起着至关重要的作用。由于很难通过分析求解，我们通过Riemannian梯度下降算法或定点算法提出了数值解。 除了检测性能外，检测器对离群值的鲁棒性也至关重要，通常可以通过影响功能对其进行分析。为遗传学矩阵引入正交基础，我们能够通过求解线性系统来分析和准确地计算相应的影响函数，这是从管理矩阵方程转换的。数值模拟表明，TBD中位数比其平均值更强大。
A novel family of geometric signal detectors are proposed through medians of the total Bregman divergence (TBD), which are shown advantageous over the conventional methods and their mean counterparts. By interpreting the observation data as Hermitian positive-definite matrices, their mean or median play an essential role in signal detection. As is difficult to be solved analytically, we propose numerical solutions through Riemannian gradient descent algorithms or fixed-point algorithms. Beside detection performance, robustness of a detector to outliers is also of vital importance, which can often be analyzed via the influence functions. Introducing an orthogonal basis for Hermitian matrices, we are able to compute the corresponding influence functions analytically and exactly by solving a linear system, which is transformed from the governing matrix equation. Numerical simulations show that the TBD medians are more robust than their mean counterparts.
