Modelling Graph Errors: Towards Robust Graph Signal Processing

The first step for any graph signal processing (GSP) procedure is to learn the graph signal representation, i.e., to capture the dependence structure of the data into an adjacency matrix. Indeed, the adjacency matrix is typically not known a priori and has to be learned. However, it is learned with errors. A little, if any, attention has been paid to modeling such errors in the adjacency matrix, and studying their effects on GSP methods. However, modeling errors in adjacency matrix will enable both to study the graph error effects in GSP and to develop robust GSP algorithms. In this paper, we therefore introduce practically justifiable graph error models. We also study, both analytically and in terms of simulations, the graph error effect on the performance of GSP methods based on the examples of more traditional different types of filtering of graph signals and less known independent component analysis (ICA) of graph signals (graph decorrelation).