作者：Nathan Mankovich Tolga Birdal
本文提出了一种新的、可证明收敛的算法，用于在弦度量下计算标志流形上一组点的滞后均值和标志中值。标志流形是一个由标志组成的数学空间，标志是向量空间中增加维数的嵌套子空间序列。flag流形是包括Stiefel和Grassmanians在内的一系列已知矩阵群的超集，使其成为各种计算机视觉问题中有用的一般对象。为了解决计算一阶标志统计量的挑战，我们首先将问题转化为一个涉及约束于Stiefel流形的辅助变量的问题。Stiefel流形是一个正交框架的空间，平均Stiefel歧管优化的数值稳定性和效率使我们能够有效地计算标志均值。通过一系列实验，我们展示了我们的方法在Grassmann和旋转平均方面的能力，以及主要成分
This paper presents a new, provably-convergent algorithm for computing theflag-mean and flag-median of a set of points on a flag manifold under thechordal metric. The flag manifold is a mathematical space consisting of flags,which are sequences of nested subspaces of a vector space that increase indimension. The flag manifold is a superset of a wide range of known matrixgroups, including Stiefel and Grassmanians, making it a general object that isuseful in a wide variety computer vision problems. To tackle the challenge of computing first order flag statistics, we firsttransform the problem into one that involves auxiliary variables constrained tothe Stiefel manifold. The Stiefel manifold is a space of orthogonal frames, andleveraging the numerical stability and efficiency of Stiefel-manifoldoptimization enables us to compute the flag-mean effectively. Through a seriesof experiments, we show the competence of our method in Grassmann and rotationaveraging, as well as principal component analysis.
论文链接：http://arxiv.org/pdf/2303.13501v1
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