Analysis of Graph Matched Filters for Higher-Order Diffusion Signals

Matched filters for signals residing on directed graphs are analyzed in this paper. In this case, the adjacency matrix is asymmetric, therefore commonly leading to nonorthogonal eigenvectors. The concept of matched filters is crucial for signal analysis, as well as for understanding convolutional neural networks (CNN) for data on graphs. We analyze the performance of graph-matched filters for diffusion signals, particularly focusing on the case when the optimal order of the matched filter and the initial vertex of signal diffusion are unknown.