Graph Learning From Signals With Smoothness Superimposed by Regressors

There is an increasing interest in processing data described by graph structures resulting in graph signal processing (GSP) and graph neural networks (GNN). One of the fundamental problems in GSP is graph learning, which uncovers the network topology from the signals measured at vertices. However, most existing approaches to graph learning merely look at the functional mapping from the smooth signals to the graph without considering signals' regressors. This letter proposes a novel algorithm (GLReg) for graph learning from smooth signals on the network and other regressors, considering the graph signals' smoothness and their relationship with other regressors. The theoretical derivation explains the proposed algorithm GLReg, and experimental tests on synthetic and real-world graphs show the effectiveness of our algorithm. The results of our study provide new insight into the graph learning model, and can be widely applied in the analysis of geographical, biomedical, and social networks.