论文标题
对称阳性半明确riemannian几何形状，并应用于域适应
Symmetric Positive Semi-definite Riemannian Geometry with Application to Domain Adaptation
论文作者
论文摘要
在本文中，我们介绍了对称阳性半明确（SPSD）矩阵的riemannian几何形状的新结果。首先，基于地球路径的现有近似值，我们引入对数图和指数图的近似值。其次，我们提出了平行运输（PT）的封闭式表达。第三，我们为一组SPSD矩阵得出一个规范表示。基于这些结果，我们提出了一种用于域适应性（DA）的算法，并在两个应用中演示了其性能：超光谱图像的融合和运动识别。
In this paper, we present new results on the Riemannian geometry of symmetric positive semi-definite (SPSD) matrices. First, based on an existing approximation of the geodesic path, we introduce approximations of the logarithmic and exponential maps. Second, we present a closed-form expression for Parallel Transport (PT). Third, we derive a canonical representation for a set of SPSD matrices. Based on these results, we propose an algorithm for Domain Adaptation (DA) and demonstrate its performance in two applications: fusion of hyper-spectral images and motion identification.
