论文标题
自适应迭代奇异值阈值算法至低级别矩阵恢复
Adaptive iterative singular value thresholding algorithm to low-rank matrix recovery
论文作者
论文摘要
近年来，从线性约束中恢复低级矩阵的问题（称为仿射基质等级最小化问题）一直引起广泛的关注。通常，仿射矩阵秩最小化问题是NP-HARD。在我们的最新工作中，研究了一个非凸位分数函数，以近似仿射矩阵秩最小化问题中的等级函数，并将NP-HARD仿射矩阵秩最小化问题转化为一个变换的仿射矩阵秩最小化问题。生成迭代奇异值阈值算法的方案，以解决正则转化的仿射矩阵秩最小化问题。但是，我们迭代奇异值阈值算法的缺点之一是，参数$ a $，它影响了在每个模拟中都需要手动确定非正规化转换的仿射矩阵最小化问题中非convex分数函数的行为。实际上，如何确定最佳参数$ a $不是一个容易的问题。相反，在本文中，我们将生成一种自适应的迭代奇异值阈值算法来解决正则转换的仿射矩阵秩最小化问题。这样做时，我们的新算法对于选择正则化参数$λ$和参数$ a $的智能将是智能的。
The problem of recovering a low-rank matrix from the linear constraints, known as affine matrix rank minimization problem, has been attracting extensive attention in recent years. In general, affine matrix rank minimization problem is a NP-hard. In our latest work, a non-convex fraction function is studied to approximate the rank function in affine matrix rank minimization problem and translate the NP-hard affine matrix rank minimization problem into a transformed affine matrix rank minimization problem. A scheme of iterative singular value thresholding algorithm is generated to solve the regularized transformed affine matrix rank minimization problem. However, one of the drawbacks for our iterative singular value thresholding algorithm is that the parameter $a$, which influences the behaviour of non-convex fraction function in the regularized transformed affine matrix rank minimization problem, needs to be determined manually in every simulation. In fact, how to determine the optimal parameter $a$ is not an easy problem. Here instead, in this paper, we will generate an adaptive iterative singular value thresholding algorithm to solve the regularized transformed affine matrix rank minimization problem. When doing so, our new algorithm will be intelligent both for the choice of the regularized parameter $λ$ and the parameter $a$.
