对称加权算法对数据矩阵补全的优化研究

Optimization of Data Matrix Completion by Symmetric Weighting Algorithm

摘要:

数据分析中存在数据集矩阵缺失，可用数据矩阵补全缺失数据元素，高效的补全数据矩阵算法可从算法精度等方面优化提升.为此提出对称加权 (SW)算法，首先，根据通用的矩阵补全模型，用正则化方法进行低秩矩阵分解补全；其次，对分解后的矩阵因子用共同的对称矩阵加权，得到新的矩阵补全模型和正则化加权函数；最后，结合块坐标下降和交替最小二乘法优化算法，迭代得到目标函数最优解，获得数据补全的最优补全矩阵.仿真结果表明，与APALM，IRSVF和IRNN算法相比，对称加权算法在数据矩阵补全的精度和算法收敛速度方面均有较好提升.

Abstract:

Data set matrix is missing in data analysis, data elements can be completed by data matrix, and the efficient completion data matrix algorithm can be optimized and improved from the aspects of algorithm accuracy. A Symmetric Weighting (SW) algorithm is proposed. Firstly, according to the general matrix completion model, the regularization method is used to complete the low-rank matrix decomposition. Secondly, a new matrix completion model and a regularization weighting function are obtained by weighting the decomposed matrix factors with a common symmetric matrix. Finally, using block coordinate descent and alternate least square optimization algorithm, the optimal solution of the objective function is obtained iteratively, and the optimal completion matrix of data completion is obtained. Compared with APALM, IRSVF and IRNN, the symmetric weighting algorithm has better improvement in the precision and convergence speed of data matrix completion.