Generative Topographic Mapping Based Aggregation Function for GCNN

Paolo Frazzetto, Luca Pasa, Nicolò Navarin, Alessandro Sperduti

Keywords: Graph Neural Network, Generative Topographic Mapping, Node Aggregation

Abstract: In Graph Convolutional Neural Networks, the capability of learning the representation of graph nodes comes at hand when dealing with one of the many graph analysis tasks, namely the prediction of node properties. Furthermore, node-level representations can be aggregated to obtain a single graph-level representation and predictor. Such aggregator functions are essential to retaining the most information about graph topology. This work explores an alternative route for the definition of 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 project them in a low-dimensional space, while retaining the information about their mutual similarity. 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 benchmark datasets show that this approach achieves competitive predictive performances with respect to the commonly adopted aggregation architectures present in the literature while retaining a well-grounded theoretical framework.