论文标题
低级矩阵完成的两阶基基算法
A two-phase rank-based algorithm for low-rank matrix completion
论文作者
论文摘要
矩阵完成旨在从其条目的一小部分中恢复未知的低级矩阵。在许多应用中，未知目标矩阵的等级是事先已知的。在本文中，首先，我们重新访问了最近提出的基于等级的启发式启发式，以完成“已知”矩阵完成，并建立一个条件，在该条件下，生成的序列是quasi-fejércontiongent to to solution集合。然后，通过包括一种类似于Nesterov的加速度的加速机制，我们获得了一种新的启发式方法。即使总体上不能批准这种启发式的融合，但事实证明，它可以作为一个温暖的阶段非常有用，为正则化参数提供了合适的估计值，并且是一个良好的起点，并且可以加快加速的软性算法。合成数据和实际数据的数值实验表明，所得的两阶段基于两相的算法可以恢复低级别的矩阵，其精度相对较高，比其他公认的矩阵完成算法更快。
Matrix completion aims to recover an unknown low-rank matrix from a small subset of its entries. In many applications, the rank of the unknown target matrix is known in advance. In this paper, first we revisit a recently proposed rank-based heuristic for "known-rank" matrix completion and establish a condition under which the generated sequence is quasi-Fejér convergent to the solution set. Then, by including an acceleration mechanism similar to Nesterov's acceleration, we obtain a new heuristic. Even though the convergence of such heuristic cannot be granted in general, it turns out that it can be very useful as a warm-start phase, providing a suitable estimate for the regularization parameter and a good starting-point, to an accelerated Soft-Impute algorithm. Numerical experiments with both synthetic and real data show that the resulting two-phase rank-based algorithm can recover low-rank matrices, with relatively high precision, faster than other well-established matrix completion algorithms.
