Low-rank matrix completion is the task of recovering unknown entries of a matrix by assuming that the true matrix admits a good low-rank approximation. Sometimes additional information about the variables is known, and incorporating this information into a matrix completion model can lead to a better completion quality. We consider the situation where information between the column/row entities of the matrix is available as a weighted graph. In this framework, we address the problem of completing missing entries in air temperature data recorded by weather stations. We construct test sets by holding back data at locations that mimic real-life gaps in weather data. On such test sets, we show that adequate spatial and temporal graphs can significantly improve the accuracy of the completion obtained by graph-regularized low-rank matrix completion methods.

翻译：低秩矩阵补全是一种通过假设真实矩阵具有良好低秩近似来恢复未知矩阵条目的任务。有时，关于变量的额外信息是已知的，将这些信息纳入矩阵补全模型可以提高补全质量。我们考虑一种情形，即矩阵列/行实体之间的信息以加权图的形式可用。在此框架下，我们解决了由气象站记录的空气温度数据中缺失条目的补全问题。我们通过保留模拟气象数据真实缺失位置的数据来构建测试集。在这些测试集上，我们证明了适当的时空图可以显著提高通过图正则化低秩矩阵补全方法获得的补全准确性。