基于加权Schatten-1/2范数的低秩矩阵近似算法
Weighted Schatten-1/2 Norm Minimization for Low-Rank Matrix Approximation
DOI: 10.12677/PM.2021.116114, PDF,   
作者: 王 素：南京航空航天大学理学院数学系，江苏 南京；顾颖菁：南京晓庄学院商学院，江苏 南京；袁 泉：南京航空航天大学理学院数学系，江苏 南京；飞行器数学建模与高性能计算工业和信息化部重点实验室(南京航空航天大学)，江苏 南京
关键词: 加权Schatten-1/2拟范数；低秩矩阵近似；不动点迭代算法；约化奇异值分解；非凸正则化；The Weighted Schatten-1/2 Norm； Low-Rank Matrix Approximation； Fixed Point Iterative Algorithm； Reduced Singular Value Decomposition； Non-Convex Regularization
摘要: 本文提出加权的Schatten-1/2拟范数求解低秩矩阵近似问题，该模型以加权的Schatten-1/2拟范数为目标函数，观测矩阵为约束。通过基于阈值的加权不动点迭代算法求解。该方法通过分配不同权值体现奇异值的重要性可更好地近似原来的低秩假设。另一方面，针对奇异值计算量大的问题引入约化奇异值分解。数值实验结果表明，该方法具有较快的收敛速度。
Abstract: In this paper, the low-rank matrix approximation problem is discussed with a weighted Schatten quasi-norm as the objective function, constrained by partial obtained data. The weights are in-troduced to measure the importance of different rank components. A weighted fixed point iterative thresholding algorithm is proposed based on the fixed point representation theory. The con-vergence analysis of the algorithm is provided. Numerical examples illustrate the effciency of our method.
文章引用：王素, 顾颖菁, 袁泉. 基于加权Schatten-1/2范数的低秩矩阵近似算法[J]. 理论数学, 2021, 11(6): 998-1009. https://doi.org/10.12677/PM.2021.116114

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