求解矩阵补全问题的三分解方法

Matrix Completion by Using Tri-factorization Method

在机器学习、图像处理等研究领域,矩阵补全主要用于恢复一个完整的低秩矩阵。考虑到计算迭代过程中,每一步均需要进行奇异值分解,若矩阵维数过大,则计算复杂度非常高。为降低计算复杂度,本文将矩阵三分解方法应用到鲁棒矩阵补全问题中,并应用交替方向乘子法对其进行求解。最后利用人脸识别的实际数据,通过数值实验验证了方法的有效性。

Matrix completion（MC）has a wide range of applications in machine learning and image processing to recover a low-rank matrix from a partially observed data entries.Considering the need for singular value decomposition in each calculation of iteration,too large matrices will lead to high computational cost.To mitigate the computational cost,the tri-factorization method（TFM）was applied to the robust MC（RMC）problem in this paper.Then,it was solved by using the alternating direction method of multipliers.Finally,numerical experiments were conducted based on real data of face recognition and the experimental results verified the encouraging performance of the proposed method for face recognition task.