### Abstract

Estimating missing values in visual data is a challenging problem in computer vision, which can be considered as a low rank matrix approximation problem. Most of the recent studies use the nuclear norm as a convex relaxation of the rank operator. However, by minimizing the nuclear norm, all the singular values are simultaneously minimized, and thus the rank can not be well approximated in practice. In this paper, we propose a novel matrix completion algorithm based on the Truncated Nuclear Norm Regularization (TNNR) by only minimizing the smallest N-r singular values, where N is the number of singular values and r is the rank of the matrix. In this way, the rank of the matrix can be better approximated than the nuclear norm. We further develop an efficient iterative procedure to solve the optimization problem by using the alternating direction method of multipliers and the accelerated proximal gradient line search method. Experimental results in a wide range of applications demonstrate the effectiveness of our proposed approach.

Original language | English (US) |
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Title of host publication | Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition |

Pages | 2192-2199 |

Number of pages | 8 |

DOIs | |

State | Published - 2012 |

Event | 2012 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2012 - Providence, RI, United States Duration: Jun 16 2012 → Jun 21 2012 |

### Other

Other | 2012 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2012 |
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Country | United States |

City | Providence, RI |

Period | 6/16/12 → 6/21/12 |

### Fingerprint

### ASJC Scopus subject areas

- Software
- Computer Vision and Pattern Recognition

### Cite this

*Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition*(pp. 2192-2199). [6247927] https://doi.org/10.1109/CVPR.2012.6247927

**Matrix completion by Truncated Nuclear Norm Regularization.** / Zhang, Debing; Hu, Yao; Ye, Jieping; Li, Xuelong; He, Xiaofei.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition.*, 6247927, pp. 2192-2199, 2012 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2012, Providence, RI, United States, 6/16/12. https://doi.org/10.1109/CVPR.2012.6247927

}

TY - GEN

T1 - Matrix completion by Truncated Nuclear Norm Regularization

AU - Zhang, Debing

AU - Hu, Yao

AU - Ye, Jieping

AU - Li, Xuelong

AU - He, Xiaofei

PY - 2012

Y1 - 2012

N2 - Estimating missing values in visual data is a challenging problem in computer vision, which can be considered as a low rank matrix approximation problem. Most of the recent studies use the nuclear norm as a convex relaxation of the rank operator. However, by minimizing the nuclear norm, all the singular values are simultaneously minimized, and thus the rank can not be well approximated in practice. In this paper, we propose a novel matrix completion algorithm based on the Truncated Nuclear Norm Regularization (TNNR) by only minimizing the smallest N-r singular values, where N is the number of singular values and r is the rank of the matrix. In this way, the rank of the matrix can be better approximated than the nuclear norm. We further develop an efficient iterative procedure to solve the optimization problem by using the alternating direction method of multipliers and the accelerated proximal gradient line search method. Experimental results in a wide range of applications demonstrate the effectiveness of our proposed approach.

AB - Estimating missing values in visual data is a challenging problem in computer vision, which can be considered as a low rank matrix approximation problem. Most of the recent studies use the nuclear norm as a convex relaxation of the rank operator. However, by minimizing the nuclear norm, all the singular values are simultaneously minimized, and thus the rank can not be well approximated in practice. In this paper, we propose a novel matrix completion algorithm based on the Truncated Nuclear Norm Regularization (TNNR) by only minimizing the smallest N-r singular values, where N is the number of singular values and r is the rank of the matrix. In this way, the rank of the matrix can be better approximated than the nuclear norm. We further develop an efficient iterative procedure to solve the optimization problem by using the alternating direction method of multipliers and the accelerated proximal gradient line search method. Experimental results in a wide range of applications demonstrate the effectiveness of our proposed approach.

UR - http://www.scopus.com/inward/record.url?scp=84866667614&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84866667614&partnerID=8YFLogxK

U2 - 10.1109/CVPR.2012.6247927

DO - 10.1109/CVPR.2012.6247927

M3 - Conference contribution

SN - 9781467312264

SP - 2192

EP - 2199

BT - Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition

ER -