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Graph Convolutional Networks (GCNs) have proven to be successful tools forsemi-supervised classification on graph-based datasets. We propose a new GCNvariant whose three-part filter space is targeted at dense graphs. Examplesinclude Gaussian graphs for 3D point clouds with an increased focus onnon-local information, as well as hypergraphs based on categorical data. Thesegraphs differ from the common sparse benchmark graphs in terms of the spectralproperties of their graph Laplacian. Most notably we observe large eigengaps,which are unfavorable for popular existing GCN architectures. Our methodovercomes these issues by utilizing the pseudoinverse of the Laplacian. Anotherkey ingredient is a low-rank approximation of the convolutional matrix,ensuring computational efficiency and increasing accuracy at the same time. Weoutline how the necessary eigeninformation can be computed efficiently in eachapplications and discuss the appropriate choice of the only metaparameter, theapproximation rank. We finally showcase our method's performance regardingruntime and accuracy in various experiments with real-world datasets.

Pseudoinverse Graph Convolutional Networks: Fast Filters Tailored for Large Eigengaps of Dense Graphs and Hypergraphs