sis 23(3): e6

Research Article

Matrix Completion via Successive Low-rank Matrix Approximation

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  • @ARTICLE{10.4108/eetsis.v10i3.2878,
        author={Jin Wang and Zeyao Mo},
        title={ Matrix Completion via Successive Low-rank Matrix Approximation},
        journal={EAI Endorsed Transactions on Scalable Information Systems},
        volume={10},
        number={3},
        publisher={EAI},
        journal_a={SIS},
        year={2023},
        month={1},
        keywords={matrix completion, low-rank matrix approximation, hard thresholding},
        doi={10.4108/eetsis.v10i3.2878}
    }
    
  • Jin Wang
    Zeyao Mo
    Year: 2023
    Matrix Completion via Successive Low-rank Matrix Approximation
    SIS
    EAI
    DOI: 10.4108/eetsis.v10i3.2878
Jin Wang1,*, Zeyao Mo2
  • 1: Institute of Applied Physics and Computational Mathematics
  • 2: China Academy of Engineering Physics
*Contact email: wangjin910103@163.com

Abstract

In this paper, a successive low-rank matrix approximation algorithm is presented for the matrix completion (MC) based on hard thresholding method, which approximate the optimal low-rank matrix from rank-one matrix step by step. The algorithm enables the distance between the matrix with the observed elements and the projection on low-rank manifold to be minimum. The optimal low-rank matrix with observed elements is obtained when the distance is zero. In theory, convergence and convergent error of the new algorithm are analyzed in detail. Furthermore, some numerical experiments show that the algorithm is more effective in CPU time and precision than the orthogonal rank-one matrix pursuit(OR1MP) algorithm and the augmented Lagrange multiplier (ALM) method when the sampling rate is low.