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

Feiping Nie; Rui Zhang; Xuelong Li

doi:10.1007/s11432-016-9021-9

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

Feiping Nie, Rui Zhang, Xuelong Li

School of Artificial Intelligence, OPtics and Electronics

Research output: Contribution to journal › Article › peer-review

176 Scopus citations

Abstract

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

Original language	English
Article number	112101
Journal	Science China Information Sciences
Volume	60
Issue number	11
DOIs	https://doi.org/10.1007/s11432-016-9021-9
State	Published - 1 Nov 2017

Keywords

Stiefel manifold
orthogonal least square regression
power iteration
procrustes problem
quadratic problem

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10.1007/s11432-016-9021-9

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title = "A generalized power iteration method for solving quadratic problem on the Stiefel manifold",

abstract = "In this paper, we first propose a novel generalized power iteration (GPI) method to solve the quadratic problem on the Stiefel manifold (QPSM) as minWTW=I Tr(WTAW − 2WTB) along with the theoretical analysis. Accordingly, its special case known as the orthogonal least square regression (OLSR) is under further investigation. Based on the aforementioned studies, we then majorly focus on solving the unbalanced orthogonal procrustes problem (UOPP). As a result, not only a general convergent algorithm is derived theoretically but the efficiency of the proposed approach is verified empirically as well.",

keywords = "Stiefel manifold, orthogonal least square regression, power iteration, procrustes problem, quadratic problem",

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AU - Zhang, Rui

AU - Li, Xuelong

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N2 - In this paper, we first propose a novel generalized power iteration (GPI) method to solve the quadratic problem on the Stiefel manifold (QPSM) as minWTW=I Tr(WTAW − 2WTB) along with the theoretical analysis. Accordingly, its special case known as the orthogonal least square regression (OLSR) is under further investigation. Based on the aforementioned studies, we then majorly focus on solving the unbalanced orthogonal procrustes problem (UOPP). As a result, not only a general convergent algorithm is derived theoretically but the efficiency of the proposed approach is verified empirically as well.

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KW - orthogonal least square regression

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JO - Science China Information Sciences

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ER -

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

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Keywords

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