矩阵填充的子空间逼近法

A subspace-approximating algorithm for matrix completion

本文提出了一种矩阵填充的子空间逼近法.该算法以奇异值分解的子空间逼近为基础,运用二次规划技术产生子空间中最接近的可行矩阵,从而获得较好的可行矩阵.该算法通过阈值的奇异值个数逐步减少达到子空间的降秩,最后得到最优低秩矩阵.本文证明了在一定条件下子空间逼近法是收敛的.通过与增广Lagrange乘子算法和正交秩1矩阵逼近法进行随机实验对比,本文所提方法在CPU时间和低秩性上均更有效.

In this paper, we propose a new subspace-approximating algorithm for matrix completion based on the subspace-approximating of the singular value decomposition. Then we use quadratic programming to produce the closest and the best feasible matrix in the subspace. This algorithm can achieve the reduction of the rank of the subspace by gradually reducing the number of the singular value of the thresholding and get the optimal low-rank matrix. It is proved that the subspace-approximating algorithm is convergent under some conditions.Besides, compared with the augmented Lagrange multiplier algorithm and orthogonal rank-one matrix pursuit algorithm by random experiments, the proposed algorithm is more effective in the CPU time and the low-rank property.