Title :
A method to compute averages over the compact Stiefel manifold
Author :
Kaneko, T. ; Tanaka, T. ; Fiori, S.
Author_Institution :
Dept. of Electr. & Electron. Eng., Tokyo Univ. of Agric. & Technol., Koganei, Japan
Abstract :
The aim of the present contribution is to extend the algorithm introduced in the paper S. Fiori and T. Tanaka, “An algorithm to compute averages on matrix Lie groups,” IEEE Transactions on Signal Processing, Vol. 57, No. 12, pp. 4734 - 4743, December 2009, to compute averages over the Stiefel manifold. The idea underlying the developed algorithms is that points on the Stiefel manifold are mapped onto a tangent space, where the average is taken, and then the average point on the tangent space is projected back to the Stiefel manifold. Based on this idea, a fixed-point algorithm is developed, and numerical examples are shown to support the analysis.
Keywords :
Lie groups; matrix algebra; signal processing; average computation algorithm; compact Stiefel manifold; fixed-point algorithm; matrix Lie groups; tangent space; Algorithm design and analysis; Equations; Manifolds; Mathematical model; Matrix decomposition; Signal processing algorithms; Symmetric matrices; Averaging on matrix manifolds; Manifold retraction; Matrix manifolds; QR-decomposition;
Conference_Titel :
Acoustics, Speech and Signal Processing (ICASSP), 2012 IEEE International Conference on
Conference_Location :
Kyoto
Print_ISBN :
978-1-4673-0045-2
Electronic_ISBN :
1520-6149
DOI :
10.1109/ICASSP.2012.6288752