关键词: 矩阵填充, 符号矩阵, 增广Lagrange乘子算法, 遗传算法

Abstract: Matrix completion is one of research hotspots in recent years. Especially, the problem of sign matrix completion has wide applications in fields such as biomedical. In this paper, based on the singular value threshold algorithm, we propose a modified augmented Lagrange multiplier algorithm for sign matrix completion. The threshold matrix generated at each step of the modified algorithm is projected to form a new sign matrix, which forms an iteration on the discrete set of sign matrices. Meanwhile, we prove that under the reasonable conditions, the modified algorithm converges when the penalty factor is large enough. Finally, the numerical examples show that compared with the augmented Lagrange multiplier algorithm and the genetic algorithm, the modified algorithm has obvious advantages in terms of time and error.

Key words: matrix completion, sign matrix, augmented Lagrange algorithm, genetic algorithm