基于加权核范数的低秩矩阵补全算法研究  

Low-Rank Matrix Completion with Weighted Nuclear Norm Regularizer

作　　者：石莹[1] 黄华[2] 王智[3] 高超[4] SHI Ying;HUANG Hua;WANG Zhi;GAO Chao(Office of Information Technology,Southwest University,Chongqing 400715,China;Modern Education Technology Center,Chongqing Vocational Institute of Engineering,Chongqing 402260,China;College of Computer and Information Science,Southwest University,Chongqing 400715,China;School of Artificial Intelligence,Northwestern Polytechnical University,Xi'an 710072,China)

机构地区：[1]西南大学信息化建设办公室,重庆400715 [2]重庆工程职业技术学院,现代教育技术中心,重庆402260 [3]西南大学计算机与信息科学学院,重庆400715 [4]西北工业大学光电与智能研究院,西安710072

出　　处：《西南大学学报（自然科学版）》2022年第5期192-202,共11页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金项目(61976181).

摘　　要：利用加权核范数去松弛原始低秩极小化问题,基于Soft-Impute算法思想提出WNNM-Impute算法.通过引入不精确的近邻算子极大地降低WNNM-Impute算法的时间复杂度,从而使得算法收敛更快.同时,在算法中引入Nesterov加速策略,使得算法的总体迭代次数进一步减少.大量的实验结果表明,所提算法能得到更精确的解且拥有比Soft-Impute和大多数对比算法更快的收敛速率.Low rank matrix completion is a most basic problem in machine learning and data analysis.It plays a key role in solving many important problems,such as collaborative filtering,dimensionality reduction,multi-task learning and pattern recognition.In this work,we employ the weighted nuclear norm to relax the rank function.Inspired by the idea of Soft-Impute,we proposed WNNM-Impute algorithm by using inexact proximal operator and Nesterov's rule.Experiments delivered very encouraging results in terms of the quality of achieved solution and the processing time required.

关 键 词：低秩矩阵补全 Soft-Impute算法 Nesterov优化理论 

分 类 号：TN911.72[电子电信—通信与信息系统]