Defining Graph Signal Distances Using an Optimal Mass Transport Framework

In this work, we propose a novel measure of distance for quantifying dissimilarities between signals observed on a graph. Building on a recently introduced optimal mass transport framework, the distance measure is formed using the second-order statistics of the graph signals, allowing for comparison of graph processes without direct access to the signals themselves, while explicitly taking the dynamics of the underlying graph into account. The behavior of the proposed distance notion is illustrated in a graph signal classification scenario, indicating attractive modeling properties, as compared to the standard Euclidean metric.