矩阵补全模型及其算法研究综述

发布时间：2018-02-23 13:43

本文关键词： 稀疏学习矩阵补全压缩感知矩阵分解随机优化　出处：《软件学报》2017年06期 　论文类型：期刊论文

【摘要】：近年来,随着压缩感知技术在信号处理领域的巨大成功,由其衍生而来的矩阵补全技术也日益成为机器学习领域的研究热点,诸多研究者针对矩阵补全问题展开了大量卓有成效的研究.为了更好地把握矩阵补全技术的发展规律,促进矩阵补全理论与工程应用相结合,针对矩阵补全模型及其算法进行了综述.首先,对矩阵补全技术进行溯源,介绍了从压缩感知到矩阵补全的自然演化历程,指出压缩感知理论的发展为矩阵补全理论的形成奠定了基础;其次,从非凸非光滑秩函数松弛的角度将现有矩阵补全模型进行分类,旨在为面向具体应用的矩阵补全问题建模提供思路;然后综述了适用于矩阵补全模型求解的代表性优化算法,其目的在于从本质上理解各种矩阵补全模型优化技巧,从而有利于面向应用问题的矩阵补全新模型求解;最后分析了矩阵补全模型及其算法目前存在的问题,提出了可能的解决思路,并对未来的研究方向进行了展望.
[Abstract]:In recent years, with the great success of compressed sensing technology in the field of signal processing, matrix complement technology derived from it has become a hot topic in the field of machine learning. Many researchers have carried out a great deal of fruitful research on the problem of matrix complement, in order to better grasp the development law of matrix complement technology and promote the combination of matrix complement theory and engineering application, This paper summarizes the matrix complement model and its algorithm. Firstly, the source of matrix complement technology is traced, and the natural evolution from compression perception to matrix complement is introduced. It is pointed out that the development of compressed perception theory lays a foundation for the formation of matrix complement theory. Secondly, the existing matrix complement models are classified from the point of view of nonconvex nonsmooth rank function relaxation. The purpose of this paper is to provide ideas for the modeling of matrix complement problems oriented to specific applications, and then summarize the representative optimization algorithms suitable for solving matrix complement models, the purpose of which is to understand various optimization techniques of matrix complement models in essence. Finally, the problems existing in the matrix complement model and its algorithm are analyzed, the possible solutions are put forward, and the future research direction is prospected.
【作者单位】：南京航空航天大学计算机科学与技术学院;江苏省无线传感网高技术研究重点实验室(南京邮电大学);南京邮电大学计算机学院;
【基金】：国家自然科学基金(61472186,61572263,61403208) 江苏省自然科学基金(BK20161516,BK20151511) 中国博士后科学基金(2015M581794) 江苏省高校自然科学研究面上项目(15KJB520027) 江苏省博士后科研资助计划(1501023C) 南京邮电大学校级科研基金(NY214127,NY215097)~~
【分类号】：TP181

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