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Most of nowadays learning schemes neglect the data structure and useful relationships amongst the training examples. On the opposite, there are plenty of learning tasks from, amongst others, chemistry, biology, pattern recognition, and data mining that can take advantage from structural representations and from a systematic exploitation of data relationships. In this seminar, we propose a new model, called Graph Neural Network (GNN), where the input data is represented by graphs: the nodes denote concepts or objects, while the edges represent their relationships. GNNs can process general kinds of graphs, directed, undirected, cyclic, acyclic, positional and non positional graphs. It has been proved that GNNS have a sort of universal approximation property and can approximate most of the practically useful functions on graphs. We also report the experimental results obtained on some applications.

Franco Scarselli received the Laurea degree with honours in computer science from the University of Pisa and the a PhD degree in computer science and automation from the University of Florence. After the PhD he has been supported by foundations of private and public companies and by a postdoc of the University of Florence. In 1999, he moved to the University of Siena where he was initially a research associate and, presently, an associate professor at the department of Information Engineering. Franco Scarselli is author of more than 50 journal and conference papers. He served as a referee for several journals and conferences including IEEE transactions on Knowledge and Data Engineering, IEEE Transactions on Neural Networks, IEEE Transactions on Pattern Analysis and Machine Learning, Neural Computation, and Neural Networks. He has been has been involved in more than 20 research projects focused on software engineering, neural networks and information retrieval founded by Italian Ministry of Education (MIUR and CONFIN schemes), University of Siena (PAR scheme), Australian Research Council (linkage international and discovery schemes), European Commission and non--governative companies.