LookHops: light multi-order convolution and pooling for graph classification

Stacked convolution and pooling layers enable Convolutional Neural Networks (CNNs) to learn hierarchical representation of grid-like data[1], where the convolution extracts local patterns of the data and the pooling layers reduce the computation cost by compressing the data shape. Because both of the two operations are defined on planar grids in Euclidean domains, they cannot be directly employed in graph data, which is a more general case and widely used in fields of chemical molecules, drug design and social networks. Learning the hierarchical representation of graph is a challenging problem and one of the solutions is to extend the convolution and pooling to graph. Graph convolution includes spatial and spectral methods[2, 3], both of which can be seen as a message passing process on multi-hop graphs. For implementation on graphs of massive number of nodes, 1-order convolution, represented by GCN and GAT[4, 5], become increasingly popular, but abandon part of ability to capturing complex graph pattern.