SimPool: Towards Topology Based Graph Pooling with Structural Similarity Features

Deep learning methods for graphs have seen rapid progress in recent years with much focus awarded to generalising Convolutional Neural Networks (CNN) to graph data. CNNs are typically realised by alternating convolutional and pooling layers where the pooling layers subsample the grid and exchange spatial or temporal resolution for increased feature dimensionality. Whereas the generalised convolution operator for graphs has been studied extensively and proven useful, hierarchical coarsening of graphs is still challenging since nodes in graphs have no spatial locality and no natural order. This paper proposes two main contributions, the first is a differential module calculating structural similarity features based on the adjacency matrix. These structural similarity features may be used with various algorithms however in this paper the focus and the second main contribution is on integrating these features with a revisited pooling layer DiffPool arXiv:1806.08804 to propose a pooling layer referred to as SimPool. This is achieved by linking the concept of network reduction by means of structural similarity in graphs with the concept of hierarchical localised pooling. Experimental results demonstrate that as part of an end-to-end Graph Neural Network architecture SimPool calculates node cluster assignments that functionally resemble more to the locality preserving pooling operations used by CNNs that operate on local receptive fields in the standard grid. Furthermore the experimental results demonstrate that these features are useful in inductive graph classification tasks with no increase to the number of parameters.