Learning Laplacian Matrix for Smooth Signals on Graph*

Learning a useful Laplacian matrix plays a significant role in graph learning. This paper focuses on smoothness analysis, which leads to the concept of total variation (TV) on graphs, a new learning Laplacian matrix framework and solving it via convex optimization techniques. We show that smoothness analysis leads to an another form that gives a more sophisticated characterization for smooth signals. This unified theoretical framework can learn a meaningful Laplacian matrix by the constraint of total variation. In our experiments, this framework is demonstrated by using three different data sets.