A generalized power iteration method for solving quadratic problem on the Stiefel manifold

摘要

In this paper, we first propose a novel generalized power iteration method(GPI) to solve the quadratic problem on the Stiefel manifold (QPSM) asmin_{W^TW=I}Tr(W^TAW-2W^TB) along with the theoretical analysis. Accordingly,its special case known as the orthogonal least square regression (OLSR) isunder further investigation. Based on the aforementioned studies, we then castmajor focus on solving the unbalanced orthogonal procrustes problem (UOPP). Asa result, not only a general convergent algorithm is derived theoretically butthe efficiency of the proposed approach is verified empirically as well.