Supervised Neural Network Models for Processing Graphs

In this chapter, we will show how an agent based on artificial neural networks (ANNs) can be designed in order to naturally process structured input data en- coded as graphs. Graph Neural Networks (GNNs) [23] are an extension of classical MultiLayer Perceptrons (MLPs) that accept input data encoded as general undi- rected/directed labeled graphs. GNNs are provided with a supervised learning al- gorithm that, beside the classical input-output data fitting measure, incorporates a criterion aimed at the development of a contractive dynamics, in order to properly process the cycles in the input graph. A GNN processes a graph in input and it can be naturally employed to compute an output for each node in the graph (node–focused computation). The training examples are provided as graphs for which supervisions are given as output target values for a subset of their nodes. This processing scheme can be adapted to perform a graph–based computation in which only one output is computed for the whole graph.