Pseudoinverse Graph Convolutional Networks: Fast Filters Tailored for Large Eigengaps of Dense Graphs and Hypergraphs
This addresses a specific bottleneck for researchers and practitioners working with dense graphs like 3D point clouds and hypergraphs, offering an incremental improvement tailored to these spectral properties.
The paper tackles the problem of Graph Convolutional Networks (GCNs) performing poorly on dense graphs and hypergraphs due to large eigengaps in the graph Laplacian, proposing a new GCN variant that uses the pseudoinverse of the Laplacian and low-rank approximations to improve accuracy and runtime in experiments on real-world datasets.
Graph Convolutional Networks (GCNs) have proven to be successful tools for semi-supervised classification on graph-based datasets. We propose a new GCN variant whose three-part filter space is targeted at dense graphs. Examples include Gaussian graphs for 3D point clouds with an increased focus on non-local information, as well as hypergraphs based on categorical data. These graphs differ from the common sparse benchmark graphs in terms of the spectral properties of their graph Laplacian. Most notably we observe large eigengaps, which are unfavorable for popular existing GCN architectures. Our method overcomes these issues by utilizing the pseudoinverse of the Laplacian. Another key ingredient is a low-rank approximation of the convolutional matrix, ensuring computational efficiency and increasing accuracy at the same time. We outline how the necessary eigeninformation can be computed efficiently in each applications and discuss the appropriate choice of the only metaparameter, the approximation rank. We finally showcase our method's performance regarding runtime and accuracy in various experiments with real-world datasets.