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

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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 \(min_{W^{T}W=I}\) Tr(W T AW − 2W T B) 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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Authors and Affiliations

  1. School of Computer Science and Center for OPTical IMagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University, Xi’an, 710072, China

    Feiping Nie & Rui Zhang

  2. Center for OPTical IMagery Analysis and Learning (OPTIMAL), State Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an, 710119, China

    Xuelong Li

Authors
  1. Feiping Nie
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  2. Rui Zhang
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  3. Xuelong Li
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Correspondence to Feiping Nie or Rui Zhang.

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Nie, F., Zhang, R. & Li, X. A generalized power iteration method for solving quadratic problem on the Stiefel manifold. Sci. China Inf. Sci. 60, 112101 (2017). https://doi.org/10.1007/s11432-016-9021-9

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  • DOI: https://doi.org/10.1007/s11432-016-9021-9

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