- Keywords: Graph Convolutional Networks, Filter Representation Power, Graph Polynomial Filters
- Abstract: We introduce a second-order graph convolution (SoGC), a maximally localized kernel, that can express a polynomial spectral filter with arbitrary coefficients. We contrast our SoGC with vanilla GCN, first-order (one-hop) aggregation, and higher-order (multi-hop) aggregation by analyzing graph convolutional layers via generalized filter space. We argue that SoGC is a simple design capable of forming the basic building block of graph convolution, playing the same role as $3 \times 3$ kernels in CNNs. We build purely topological Second-Order Graph Convolutional Networks (SoGCN) and demonstrate that SoGCN consistently achieves state-of-the-art performance on the latest benchmark. Moreover, we introduce the Gated Recurrent Unit (GRU) to spectral GCNs. This explorative attempt further improves our experimental results.
- One-sentence Summary: We introduce a second-order graph convolution (SoGC), a maximally localized kernel, that can express a polynomial spectral filter of order $K$ with arbitrary coefficients.
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