Empirical Arithmetic Averaging Over the Compact Stiefel Manifold
Empirical Arithmetic Averaging Over the Compact Stiefel Manifold
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DOI：
10.1109/tsp.2012.2226167
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发表时间：
2013-02-01
影响因子：
5.4
通讯作者：
Tanaka, Toshihisa
中科院分区：
文献类型：
--
作者：
Kaneko, Tetsuya;Fiori, Simone;Tanaka, Toshihisa
本研究工作的目的是研究算法来计算有限集的样本点的经验平均的Stiefel流形上的推广的概念，毕达哥拉斯的算术平均的真实的线到一个弯曲的流形。所开发的算法的基本思想是，Stiefel流形上的采样点被映射到一个切空间上，在那里取平均值，然后通过适当的映射将切空间上的平均点带回Stiefel流形。数值实验结果显示和评论，以说明所提出的方法的数值行为。所得到的数值结果证实，开发的算法收敛稳定，在几个迭代，他们能够科普相对较大规模的问题。
The aim of the present research work is to investigate algorithms to compute empirical averages of finite sets of sample-points over the Stiefel manifold by extending the notion of Pythagoras' arithmetic averaging over the real line to a curved manifold. The idea underlying the developed algorithms is that sample-points on the Stiefel manifold get mapped onto a tangent space, where the average is taken, and then the average point on the tangent space is brought back to the Stiefel manifold, via appropriate maps. Numerical experimental results are shown and commented on in order to illustrate the numerical behaviour of the proposed procedure. The obtained numerical results confirm that the developed algorithms converge steadily and in a few iterations and that they are able to cope with relatively large-size problems.