LanczosNet: Multi-Scale Deep Graph Convolutional Networks

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}. read more

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Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Node Classification CiteSeer (0.5%) AdaLanczosNet Accuracy 53.8% # 6
Node Classification CiteSeer (0.5%) LanczosNet Accuracy 53.2% # 7
Node Classification CiteSeer (1%) LanczosNet Accuracy 61.3% # 8
Node Classification CiteSeer (1%) AdaLanczosNet Accuracy 63.3% # 6
Node Classification CiteSeer with Public Split: fixed 20 nodes per class AdaLanczosNet Accuracy 68.7% # 27
Node Classification CiteSeer with Public Split: fixed 20 nodes per class LanczosNet Accuracy 66.2% # 30
Node Classification Cora (0.5%) LanczosNet Accuracy 58.1% # 9
Node Classification Cora (0.5%) AdaLanczosNet Accuracy 60.8% # 7
Node Classification Cora (1%) AdaLanczosNet Accuracy 67.5% # 7
Node Classification Cora (1%) LanczosNet Accuracy 66.1% # 9
Node Classification Cora (3%) AdaLanczosNet Accuracy 77.7% # 7
Node Classification Cora (3%) LanczosNet Accuracy 76.3% # 10
Node Classification Cora with Public Split: fixed 20 nodes per class AdaLanczosNet Accuracy 80.4% # 25
Node Classification Cora with Public Split: fixed 20 nodes per class LanczosNet Accuracy 79.5% # 27
Node Classification PubMed (0.03%) AdaLanczosNet Accuracy 61% # 6
Node Classification PubMed (0.03%) LanczosNet Accuracy 60.4% # 8
Node Classification PubMed (0.05%) LanczosNet Accuracy 68.8% # 6
Node Classification PubMed (0.05%) AdaLanczosNet Accuracy 66% # 8
Node Classification PubMed (0.1%) LanczosNet Accuracy 73.4% # 5
Node Classification PubMed (0.1%) AdaLanczosNet Accuracy 72.8% # 9
Node Classification PubMed with Public Split: fixed 20 nodes per class AdaLanczosNet Accuracy 78.1% # 22
Node Classification PubMed with Public Split: fixed 20 nodes per class LanczosNet Accuracy 78.3% # 21
Quantum Chemistry Regression Quantum Chemistry Regression LanczosNet Test MAE 9.58 # 1
Validation MAE 9.65 # 1

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