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Abstract
We propose a novel Riemannian preconditioning approach for the tensor completion problem with rank constraint. A Riemannian metric or inner product is proposed that exploits the least-squares structure of the cost function and takes into account the structured symmetry in Tucker decomposition. The specific metric allows to use the versatile framework of Riemannian optimization on quotient manifolds to develop a preconditioned nonlinear conjugate gradient algorithm for the problem. To this end, concrete matrix representations of various optimization-related ingredients are listed. Numerical comparisons suggest that our proposed algorithm robustly outperforms state-of-the-art algorithms across different problem instances encompassing various synthetic and real-world datasets.
Journal
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- 第78回全国大会講演論文集
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第78回全国大会講演論文集 2016 (1), 225-226, 2016-03-10
東京 : 電子情報通信学会
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Keywords
Details 詳細情報について
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- CRID
- 1050011097154844032
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- NII Article ID
- 170000163028
- 40020736660
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- NII Book ID
- AN00349328
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- ISSN
- 09135685
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- NDL BIB ID
- 027107747
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- Text Lang
- en
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- Article Type
- conference paper
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- Data Source
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- IRDB
- NDL
- CiNii Articles