Graph-Based Matrix Completion Applied to Weather Data
Benoît Loucheur P. -A. Absil Michel Journée
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.