Quantum-based subgraph convolutional neural networks
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.
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| Task | Dataset | Model | Metric Name | Metric Value | Global Rank | Benchmark |
|---|---|---|---|---|---|---|
| Graph Classification | MUTAG | QS-CNNs (Quantum Walk) | Accuracy | 93.13% | # 11 | |
| Accuracy (10-fold) | 93.13 | # 2 | ||||
| Graph Classification | PROTEINS | DS-CNNs (Random Walk) | Accuracy | 78.35% | # 16 | |
| Graph Classification | PROTEINS | QS-CNNs (Quantum Walk) | Accuracy | 78.80% | # 11 |
