Matrix Completion via Successive Low-rank Matrix Approximation

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-01-04 DOI:10.4108/eetsis.v10i3.2878

Jin Wang, Z. Mo

引用次数: 0

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.

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通过逐次低秩矩阵逼近的矩阵补全

本文提出了一种基于硬阈值法的矩阵补全的逐次低秩矩阵逼近算法，该算法从秩一矩阵逐次逼近最优低秩矩阵。该算法使矩阵与观测元素之间的距离与低秩流形上的投影之间的距离最小。当距离为零时，得到具有观测元素的最优低秩矩阵。从理论上详细分析了新算法的收敛性和收敛误差。数值实验表明，当采样率较低时，该算法在CPU时间和精度上都优于正交秩一矩阵追踪(OR1MP)算法和增广拉格朗日乘子(ALM)方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.