Topology preserving maps as aggregations for Graph Convolutional Neural Networks

In Graph Convolutional Neural Networks, the capability of learning the representation of graph nodes comes at hand when dealing with graph analysis tasks, such as predicting node properties. Furthermore, node-level representations can be aggregated to obtain a single graph-level representation and predictor. This work explores an alternative route for defining the aggregation function compared to existing approaches. We propose a graph aggregator that exploits Generative Topographic Mapping (GTM) to transform a set of node-level representations into a single graph-level one. The integration of GTM in a GCNN pipeline allows to estimate node representation probability densities and projects them in a low-dimensional space, while retaining the information about their mutual similarity and topology. A novel dedicated training procedure is specifically designed to learn from these reduced representations instead of the complete initial data. Experimental results on several graph classification datasets show that this approach achieves competitive predictive performances with respect to the commonly adopted aggregation architectures present in the literature while holding a well-grounded theoretical framework.