A Novel Spectral Graph Distance Measure and Its Applications in Biomedical Signal Processing

In many real time scenarios, it becomes necessary to compare complex networks. Graph distances measure the degree of similarity between any two networks. We conjecture that construction of the edge weight matrix of any network should consider the underlying physics of the problem. In addition to that, the selection of eigenvectors chosen for analysis also play an important role in comparing any two networks. In this paper, we explore the most naturally formed networks in various real time applications, such as tracking the transitions of brain states and real time seizure onset detection, and propose a graph distance measure based on the spectral characteristics of the edge weight matrix. We have conducted several experiments to show the efficacy of the proposed graph distance measure. It has an application in comparing any two brain networks while studying brain dynamics. Our results clearly show that the proposed graph distance outperforms the existing graph distances.