LanczosNet: Multi-Scale Deep Graph Convolutional Networks
This work addresses graph learning tasks for domains like citation networks and quantum chemistry, presenting an incremental improvement over existing deep graph networks.
The authors tackled the problem of graph convolution by proposing LanczosNet, which uses the Lanczos algorithm to construct low-rank approximations of the graph Laplacian for efficient multi-scale information exploitation and learnable spectral filters, achieving state-of-the-art performance on citation networks and the QM8 quantum chemistry dataset.
We propose the Lanczos network (LanczosNet), which uses the Lanczos algorithm to construct low rank approximations of the graph Laplacian for graph convolution. Relying on the tridiagonal decomposition of the Lanczos algorithm, we not only efficiently exploit multi-scale information via fast approximated computation of matrix power but also design learnable spectral filters. Being fully differentiable, LanczosNet facilitates both graph kernel learning as well as learning node embeddings. We show the connection between our LanczosNet and graph based manifold learning methods, especially the diffusion maps. We benchmark our model against several recent deep graph networks on citation networks and QM8 quantum chemistry dataset. Experimental results show that our model achieves the state-of-the-art performance in most tasks. Code is released at: \url{https://github.com/lrjconan/LanczosNetwork}.