一种新的基于矩阵秩序数优化的矩阵补全算法研究  

Study on the New Matrix Completion Algorithm Based on Optimal Order Number Matrix

作　　者：邱林润 李蓉蓉[1] 

机构地区：[1]广东科技学院,广东东莞523000

出　　处：《科技通报》2017年第11期155-157,228,共4页Bulletin of Science and Technology

基　　金：广东省自然科学基金资助项目(2014A030313454);2015年广东省高校重大科研项目(青年创新人才项目)项目编号(2015KQNCX188)

摘　　要：设计出一种新的基于矩阵秩序数优化的截断式核范数正则化矩阵补全算法来还原低秩矩阵的缺失数据。所设计的算法为最小化min(m,n)-r类奇异值的之和,矩阵的长度用n表示、矩阵的宽度用m表示。基于秩值为r的矩阵,其最大的r类非零的奇异值均是不受约束的,由此能获得一类针对几何矩阵秩函数的最准确的类似值。从而提出运用乘子的交替方向算法完成求解过程的优化处理。仿真实验结果表明,新的基于矩阵秩序数优化的矩阵补全算法相比核范数、矩阵分解等传统算法能够更加有效的恢复缺失信息。This paper designs a new matrix order number optimization truncated nuclear norm regularization algorithm based on matrix completion reduction of low rank matrix with missing data. The algorithm designed in this paper is to minimize the sum of min(m,n)-r class singular value, the length of the matrix is expressed by N, and the width of the matrix is expressed by M. Based on the rank of R matrix, the maximum of the R class of nonzero singular values are unconstrained, which can obtain a class of geometric matrix rank function of the most accurate similar values. In order to solve the optimization of the solution process, we put forward the alternating direction algorithm. The simulation results show that the new matrix completion algorithm based on optimal order number matrix nuclear norm matrix decomposition, compared to the traditional algorithm can effectively restore the missing information.

关 键 词：迭代序列 矩阵补全 截断式核范数正则化 几何矩阵秩函数 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]