Learning Combination of Graph Filters for Graph Signal Modeling

We study the problem of parametric modeling of network-structured signals with graph filters. To benefit from the properties of several graph shift operators simultaneously, and to enhance interpretability, we investigate combinations of parallel graph filters with different shift operators. Due to their extra degrees of freedom, these models might suffer from over-fitting. We address this problem through a weighted $\ell _2$-norm regularization formulation to perform model selection by encouraging group sparsity. What makes this formulation interesting is that it is actually a smooth convex optimization problem. Experiments on real-world data structured by undirected and directed graphs show the effectiveness of this method.