Topology Preserving Maps as Aggregations for Graph Convolutional Neural Networks

Paolo Frazzetto, Luca Pasa, Nicolò Navarin, Alessandro Sperduti

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 retain 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 nodelevel
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.