论文标题
操作员规范损失的最佳单数值收缩
Optimal singular value shrinkage for operator norm loss
论文作者
论文摘要
我们研究了通过单数值收缩来研究低级矩阵的降解。 Gavish和Donoho的最新工作构建了一个框架，用于为广泛的损失功能找到最佳的单数值收缩术。我们使用此框架来得出最佳的收缩器，以实现运算符规范损失。最佳的收缩器与Gavish和Donoho在平方矩阵中提出的收缩器相匹配，但对于所有其他纵横比，但有所不同。我们精确地量化了使用最佳收缩器的准确性增益。我们还表明，最佳收缩器在长宽比零的经典状态下会收敛到最佳的线性预测变量。
We study the denoising of low-rank matrices by singular value shrinkage. Recent work of Gavish and Donoho constructs a framework for finding optimal singular value shrinkers for a wide class of loss functions. We use this framework to derive the optimal shrinker for operator norm loss. The optimal shrinker matches the shrinker proposed by Gavish and Donoho in the special case of square matrices, but differs for all other aspect ratios. We precisely quantify the gain in accuracy from using the optimal shrinker. We also show that the optimal shrinker converges to the best linear predictor in the classical regime of aspect ratio zero.
