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Simple Spectral Graph Convolution

Graph Convolutional Networks (GCNs) have drawn significant attention and become promising methods for learning graph representations. The most GCNs suffer the performance loss when the depth of the model increases. Similarly to CNNs, without specially designed architectures, the performance of a network degrades quickly. Some researchers argue that the required neighbourhood size and neural network depth are two completely orthogonal aspects of graph representation. Thus, several methods extend the neighbourhood by aggregating k-hop neighbourhoods of nodes while using shallow neural networks. However, these methods still encounter oversmoothing, high computation and storage costs. In this paper, we use the Markov diffusion kernel to derive a variant of GCN called Simple Spectral Graph Convolution (S^2GC) which is closely related to spectral models and combines strengths of both spatial and spectral methods. Our spectral analysis shows that our simple spectral graph convolution used in S^2GC is a low-pass filter which partitions networks into a few large parts. Our experimental evaluation demonstrates that S^2GC with a linear learner is competitive in text and node classification tasks. Moreover, S^2GC is comparable to other state-of-the-art methods for node clustering and community prediction tasks.

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