Graph-Based Matrix Completion Applied to Weather Data
This work addresses data gaps in weather monitoring, which is incremental as it applies existing graph-based methods to a specific domain.
The paper tackled the problem of completing missing entries in air temperature data from weather stations by using graph-regularized low-rank matrix completion methods, showing that incorporating spatial and temporal graphs significantly improved accuracy on test sets mimicking real-life data gaps.
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.