Dynamic Signed Graph Learning

An important problem in graph signal processing (GSP) is to infer the topology of an unknown graph from a set of observations on the nodes of the graph, i.e. graph signals. Recently, graph learning (GL) approaches have been extended to learn dynamic graphs from temporal graph signals. However, existing work primarily focuses on unsigned graphs and cannot learn signed graphs, which are important data structures that can represent the similarity and dissimilarity of the nodes. In this paper, we propose a dynamic signed GL (dynSGL) method based on the assumptions that (i) at each time point signals are smooth with respect to the signed graph, i.e. signal values at two nodes connected with a positive (negative) edge are similar (dissimilar) and (ii) evolution of the graph structures is smooth across time. The performance of dynSGL is evaluated on simulated data and shown to have higher accuracy compared to static signed and dynamic unsigned GL techniques. Application of the proposed method to a financial dataset gives important insights to the time-varying changes to the interactions between stocks.