矩阵填充硬阈值算法的两种修正

doi:10.12288/szjs.s2019-0611

数值计算与计算机应用 ›› 2021, Vol. 42 ›› Issue (2): 126-133.DOI: 10.12288/szjs.s2019-0611

矩阵填充硬阈值算法的两种修正

王俊霞, 王川龙, 申倩影

太原师范学院数学系, 晋中 030619

收稿日期:2019-08-03 出版日期:2021-06-15 发布日期:2021-06-03
基金资助:
国家自然科学基金（11371275）；山西省自然科学基金（201801D121022）；山西省教改项目（J2020280）和太原师范学院教改项目（JGLX1932）资助.

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王俊霞, 王川龙, 申倩影. 矩阵填充硬阈值算法的两种修正[J]. 数值计算与计算机应用, 2021, 42(2): 126-133.

Wang Junxia, Wang Chuanlong, Shen Qianying. TWO MODIFIED ALGORITHMS FOR MATRIX COMPLETION USING HARD-THERESHODING ALGORITHM[J]. Journal on Numerica Methods and Computer Applications, 2021, 42(2): 126-133.

TWO MODIFIED ALGORITHMS FOR MATRIX COMPLETION USING HARD-THERESHODING ALGORITHM

Wang Junxia, Wang Chuanlong, Shen Qianying

Department of Mathematics, Taiyuan Normal University, Jinzhong 030619, China

Received:2019-08-03 Online:2021-06-15 Published:2021-06-03

本文提出了两种使用硬阈值进行矩阵填充的修正算法. 算法通过对迭代矩阵进行对角修正来完成矩阵填充, 其中第一种算法每步均修正, 第二种算法每两步修正一次, 并给出了算法的收敛性分析. 最后通过数值实验分别比较了两种算法与硬阈值算法填充的数值结果, 显示出了新算法的优越性.

关键词： 矩阵填充, 硬阈值, 秩最小化, 对角修正

In this paper, we propose two kinds of modified hard threshold algorithms for matrix completion. We aim to diagonally modify the iteration matrix to complete matrix completion. In the first one, matrix is modified at each step. In the second one, matrix is modified at every two steps. Convergence is discussed. Finally, by numerical experiments to compare two algorithms and hard threshold algorithm for matrix completion, we can see that new algorithms are more effective than hard threshold algorithm.

Key words: matrix completion, hard-thereshoding, minimizing the rank of the matrix, diagonally modification

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矩阵填充硬阈值算法的两种修正

TWO MODIFIED ALGORITHMS FOR MATRIX COMPLETION USING HARD-THERESHODING ALGORITHM

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