Multiscale dynamic graph signal analysis

We consider the problem of decomposing a time-varying graph signal into its constituent amplitude- and frequency-modulated components and inferring their dynamic functional connectivity structures in a data-driven manner, referred to as graph mode decomposition (GMD). The currently available method for GMD obtains static connectivity structures, limiting its applicability to real-life data. Further, the performance of the method relies critically on the accurate prior knowledge of the number of components to be extracted. We address those key limitations by presenting two approaches: (1) a two-stage method for obtaining the graph modes as well as corresponding connectivity structures by solving two separate optimization problems, and (2) a joint optimization formulation to achieve that task. The proposed optimization formulations include a prior to account for the time variation of graph edge weights. Moreover, we use a successive scheme to solve the problems which alleviates the limitation of having to specify the number of decomposed components a priori – improving the accuracy and data-driven capability while reducing the computational requirement of the methods. The performance of these methods is validated on a wide range of synthetic and real data sets. We also provide a public toolbox containing the MATLAB codes of the proposed methods.