论文标题
矩阵完成的自适应和隐式正则化
Adaptive and Implicit Regularization for Matrix Completion
论文作者
论文摘要
显式低级正则化，例如核范围的正则化已广泛用于成像科学。但是，已经发现，在各种图像处理任务中，隐式正规化优于明确的正规化。另一个问题是，固定的显式正则化将适用性限制为广泛图像，因为不同的图像有利于不同的显式正规化捕获的不同特征。因此，本文提出了一种新的自适应和隐式低级别正则化，从训练数据中动态捕获了较低的先验。我们新的自适应和隐式低级别正则化的核心是在基于Dirichlet Energy的正则化中参数化Laplacian矩阵，我们称之为正则化空气。从理论上讲，我们表明\ retwo {air}的自适应正则化增强了培训结束时的隐式正则化和消失。我们验证了空气对各种基准任务的有效性，表明空气对缺失条目不均匀的情况特别有利。该代码可以在https://github.com/lizhemin15/air-net上找到。
The explicit low-rank regularization, e.g., nuclear norm regularization, has been widely used in imaging sciences. However, it has been found that implicit regularization outperforms explicit ones in various image processing tasks. Another issue is that the fixed explicit regularization limits the applicability to broad images since different images favor different features captured by different explicit regularizations. As such, this paper proposes a new adaptive and implicit low-rank regularization that captures the low-rank prior dynamically from the training data. The core of our new adaptive and implicit low-rank regularization is parameterizing the Laplacian matrix in the Dirichlet energy-based regularization, which we call the regularization AIR. Theoretically, we show that the adaptive regularization of \ReTwo{AIR} enhances the implicit regularization and vanishes at the end of training. We validate AIR's effectiveness on various benchmark tasks, indicating that the AIR is particularly favorable for the scenarios when the missing entries are non-uniform. The code can be found at https://github.com/lizhemin15/AIR-Net.
