Multiscale Graph Scattering Transform

Graph scattering transform (GST) is mathematically-designed graph convolutional model that iteratively applies graph filter banks to achieve comprehensive feature extraction from graph signals. While GST performs excessive decomposition of graph signals in the graph spectral domain, it does not explicitly achieve multiresolution in the graph vertex domain, causing potential failure in handling graphs with hierarchical structures. To address the limitation, this work proposes novel multiscale graph scattering transform (MGST) to achieve hierarchical representations along both graph vertex and spectral domains. With recursive partitioning a graph structure, we yield multiple subgraphs at various scales and then perform scattering frequency decomposition on each subgraph. MGST finally obtains a series of representations and each of them corresponds to a specific graph vertex-spectral subband, achieving multiresolution along both graph vertex and spectral domains. In the experiments, we validate the superior empirical performances of MGST and visualize each graph vertex-spectral subband.