A smoothed rank function algorithm based Hyperbolic Tangent function for matrix completion

The matrix completion problem is to recover the matrix from its partially known samples. A recent convex relaxation of the rank minimization problem minimizes the nuclear norm instead of the rank of the matrix. In this paper, we use a smooth function-Hyperbolic Tangent function to approximate the ra...

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Vydáno v:2012 International Conference on Machine Learning and Cybernetics Ročník 4; s. 1333 - 1338
Hlavní autoři: Juan Geng, Lai-Sheng Wang, Ai-Min Fu, Qi-Qing Song
Médium: Konferenční příspěvek
Jazyk:angličtina
Vydáno: IEEE 01.07.2012
Témata:
Abstracts
Hyperbolic Tangent function Approximation
Image reconstruction
MATLAB
Nuclear norm minimization
Periodic structures
Smoothed rank function approximation
ISBN:1467314846, 9781467314848
ISSN:2160-133X
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Abstract The matrix completion problem is to recover the matrix from its partially known samples. A recent convex relaxation of the rank minimization problem minimizes the nuclear norm instead of the rank of the matrix. In this paper, we use a smooth function-Hyperbolic Tangent function to approximate the rank function, and then using gradient projection method to minimize it. Our algorithm is named as Hyperbolic Tangent function Approximation algorithm (HTA). We report numerical results for solving randomly generated matrix completion problems and image reconstruction. The numerical results suggest that significant improvement be achieved by our algorithm when compared to the previous ones. Numerical results show that accuracy of HTA is higher than that of SVT and FPC, and the requisite number of sampling to recover a matrix is typically reduced. Meanwhile we can see the power of HTA algorithm for missing data estimate in images.
AbstractList The matrix completion problem is to recover the matrix from its partially known samples. A recent convex relaxation of the rank minimization problem minimizes the nuclear norm instead of the rank of the matrix. In this paper, we use a smooth function-Hyperbolic Tangent function to approximate the rank function, and then using gradient projection method to minimize it. Our algorithm is named as Hyperbolic Tangent function Approximation algorithm (HTA). We report numerical results for solving randomly generated matrix completion problems and image reconstruction. The numerical results suggest that significant improvement be achieved by our algorithm when compared to the previous ones. Numerical results show that accuracy of HTA is higher than that of SVT and FPC, and the requisite number of sampling to recover a matrix is typically reduced. Meanwhile we can see the power of HTA algorithm for missing data estimate in images.
Author Juan Geng
Ai-Min Fu
Qi-Qing Song
Lai-Sheng Wang
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  surname: Lai-Sheng Wang
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  organization: Coll. of Sci., China Agric. Univ., Beijing, China
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  surname: Ai-Min Fu
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  organization: Coll. of Sci., China Agric. Univ., Beijing, China
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  surname: Qi-Qing Song
  fullname: Qi-Qing Song
  organization: Coll. of Sci., Guilin Univ. of Technol., Guilin, China
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Snippet The matrix completion problem is to recover the matrix from its partially known samples. A recent convex relaxation of the rank minimization problem minimizes...
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SubjectTerms Abstracts
Hyperbolic Tangent function Approximation
Image reconstruction
MATLAB
Nuclear norm minimization
Periodic structures
Smoothed rank function approximation
Title A smoothed rank function algorithm based Hyperbolic Tangent function for matrix completion
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