Quantum-based subgraph convolutional neural networks

Zhihong Zhang, Dongdong Chen, Jianjia Wang, Lu Bai, Edwin R. Hancock

Abstract: Highlights • We propose a new graph convolutional neural architecture based on a depth-based representation of graph structure which integrates both the global topological and local connectivity structures within a graph. • Depth-based subgraph convolution operation: The depth-based subgraph convolution operation scans a ‘tree’ of parameters deriving from the quantum walks on graph, which extracts local features analogous to the standard convolution operation on grid data. These local features can potentially be composed to form multi-scale structures. • Depth-based subgraph pooling operation: our depth-based subgraph pooling operation acts on the output of the preceding layer directly without any preprocessing scheme such as clustering. • Experiments on eight graph-structured datasets demonstrate that our model QS-CNNs are able to outperform fourteen state-of-the-art methods at the tasks of node classification and graph classification. Abstract This paper proposes a new graph convolutional neural network architecture based on a depth-based representation of graph structure deriving from quantum walks, which we refer to as the quantum-based subgraph convolutional neural network (QS-CNNs). This new architecture captures both the global topological structure and the local connectivity structure within a graph. Specifically, we commence by establishing a family of K-layer expansion subgraphs for each vertex of a graph by quantum walks, which captures the global topological arrangement information for substructures contained within a graph. We then design a set of fixed-size convolution filters over the subgraphs, which helps to characterise multi-scale patterns residing in the data. The idea is to apply convolution filters sliding over the entire set of subgraphs rooted at a vertex to extract the local features analogous to the standard convolution operation on grid data. Experiments on eight graph-structured datasets demonstrate that QS-CNNs architecture is capable of outperforming fourteen state-of-the-art methods for the tasks of node classification and graph classification.