基于子空间阈值追踪的矩阵修补算法  

Matrix Completion Algorithm Based on Subspace Thresholding Pursuit

作　　者：王智 王建军[1] 王文东[2] WANG Zhi;WANG Jian-jun;WANG Wen-dong(School of Mathematics and Statistics,Southwest Universit;College of Computer ＆Information Science,Southwest Universit)

机构地区：[1]西南大学数学与统计学院,重庆400715 [2]西南大学计算机与信息科学学院,重庆400715

出　　处：《计算机科学》2018年第6期193-196,215,共5页Computer Science

基　　金：国家自然科学基金(61673015);西南大学实验研究项目(SYJ2016024)资助

摘　　要：低秩矩阵修补是机器学习和数据分析中的核心问题,被广泛应用于协同过滤、降维处理、多任务学习和模式识别等领域。针对ADMiRA算法存在收敛速度慢、易陷入局部最优等缺陷,通过在SP算法的每次迭代过程中引入SVP算法,提出一种基于子空间阈值追踪的矩阵修补算法。其利用SVP算法快速收敛的特性,提升了SP算法的收敛速度,且能得到更优的解。仿真实验验证了所提算法的性能。Low rank matrix completion is the 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.Focusing on the problems that the ADMiRA may have a slow convergence rate and easily fall into local optimal drawbacks,this paper proposed a new algorithm by adding SVP into SP＇s every iteration.Through making use of SVP＇s advantage of quick convergence,the proposed algorithm improves SP＇s convergence speed,and gets better result.This algorithm was implemented and tested on several simulated datasets and image datasets.Experiments reveal very encouraging results in terms of the found quality of solution and the required processing time.

关 键 词：低秩矩阵修补 ADMiRA算法 SP算法 SVP算法 局部收敛性 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]