Learning Aligned Vertex Convolutional Networks for Graph Classification

Graph convolutional networks (GCNs) are powerful tools for graph structure data analysis. One main drawback arising in most existing GCN models is that of the oversmoothing problem, i.e., the vertex features abstracted from the existing graph convolution operation have previously tended to be indistinguishable if the GCN model has many convolutional layers (e.g., more than two layers). To address this problem, in this article, we propose a family of aligned vertex convolutional network (AVCN) models that focus on learning multiscale features from local-level vertices for graph classification. This is done by adopting a transitive vertex alignment algorithm to transform arbitrary-sized graphs into fixed-size grid structures. Furthermore, we define a new aligned vertex convolution operation that can effectively learn multiscale vertex characteristics by gradually aggregating local-level neighboring aligned vertices residing on the original grid structures into a new packed aligned vertex. With the new vertex convolution operation to hand, we propose two architectures for the AVCN models to extract different hierarchical multiscale vertex feature representations for graph classification. We show that the proposed models can avoid iteratively propagating redundant information between specific neighboring vertices, restricting the notorious oversmoothing problem arising in most spatial-based GCN models. Experimental evaluations on benchmark datasets demonstrate the effectiveness.