VEM-GCN: Topology Optimization with Variational EM for Graph Convolutional Networks
Keywords: Graph Convolutional Networks, Over-smoothing, Topology Optimization, Stochastic Block Model, Variational EM
Abstract: Over-smoothing has emerged as a severe problem for node classification with graph convolutional networks (GCNs). In the view of message passing, the over-smoothing issue is caused by the observed noisy graph topology that would propagate information along inter-class edges, and consequently, over-mix the features of nodes in different classes. In this paper, we propose a novel architecture, namely VEM-GCN, to address this problem by employing the variational EM algorithm to jointly optimize the graph topology and learn desirable node representations for classification. Specifically, variational EM approaches a latent adjacency matrix parameterized by the assortative-constrained stochastic block model (SBM) to enhance intra-class connection and suppress inter-class interaction of the observed noisy graph. In the variational E-step, graph topology is optimized by approximating the posterior probability distribution of the latent adjacency matrix with a neural network learned from node embeddings. In the M-step, node representations are learned using the graph convolutional network based on the refined graph topology for the downstream task of classification. VEM-GCN is demonstrated to outperform existing strategies for tackling over-smoothing and optimizing graph topology in node classification on seven benchmark datasets.
One-sentence Summary: This paper proposes VEM-GCN for tackling the over-smoothing issue in GCNs with topology optimization that explicitly enhances intra-class connection and suppresses inter-class interaction based on the variational EM algorithm.
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