University of Siena
Department of Information Engineering and Mathematics
Franco Scarselli

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The Graph Neural Network model

The Graph Neural Network (GNN) is a novel connectionist model particularly suited for problems whose domain can be represented by a set of patterns and relationships between them [1,2]. In those problems, a prediction about a given pattern can be carried out exploiting all the related information, which includes the pattern features, the pattern relationships and, in general, the whole graph that represents the domain. GNN peculiarity consists in its capability of making the prediction taking directly in input the domain graph, without any preprocessing. In this sense, the GNN methods is different from the common approach, which face a domain with relationship by an ad hoc preprocessing procedure that compresses into a vectorial representation all the data about a pattern. Actually, GNNs can be considered the connectionist counterpart of SVM for graphs and random fields.

GNNs have been proved to be sort of universal approximator for functions on graphs and have been applied to several problems, including spam detection, object localization in images, molecule classification.

The GNN software
The GNN simulator, along with the benchamarks used in [1,2], and a short manual is available for download in the following page.

References

Definition and properties of the GNN model
  1. F. Scarselli, M. Gori,  A. C. Tsoi, M. Hagenbuchner, G. Monfardini.The Graph Neural Network Model. IEEE Transactions on Neural Networks,  vol. 20(1); p. 61-80, 2009.
  2. F. Scarselli, M. Gori,  A. C. Tsoi, M. Hagenbuchner, G. Monfardini. Computational Capabilities of Graph Neural Networks. IEEE Transactions on Neural Networks, vol. 20(1); p. 81-102, 2009.
Applications of GNNs
  1. L. Di Noi, M. Hagenbuchner, F. Scarselli, and A. Tsoi. Solving graph data issues using a layered architecture approach with applications to web spam detection. Neural Networks, 48, pages 78-90, 2013.
  2. N. Bandinelli, B. Bianchini, and F. Scarselli. Learning long-term dependencies using layered graph neural networks. In The 2012 International Joint Conference on Neural Networks, pages 1-8, 2012.
  3. W. Uwents, G. Monfardini, H. Blockeel, M. Gori, and F. Scarselli. Neural networks for relational learning: an experimental comparison. Machine Learning, 82(3):315-349, 2011.
  4. D. Muratore, M. Hagenbuchner, F. Scarselli, and A. Tsoi. Sentence extraction by graph neural networks. Artificial Neural Networks–ICANN 2010, pages 237-246, 2010.
  5. S. Zhang, M. Hagenbuchner, F. Scarselli, and A. Tsoi. Supervised encoding of graph-of-graphs for classification and regression problems. Focused Retrieval and Evaluation, pages 449-461, 2010.
  6. V. Di Massa, G. Monfardini, L. Sarti, F. Scarselli, M. Maggini, and M. Gori. A comparison between recursive neural networks and graph neural networks. In International Joint Conference on Neural Networks, pages 778-785, July 2006.
  7. Gabriele Monfardini, Vincenzo Di Massa, Franco Scarselli, and Marco Gori. Graph neural networks for object localization. In Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 - September 1, 2006, Riva del Garda, Italy, pages 665-669, Amsterdam, The Netherlands, 2006. IOS Press.
  8. F. Scarselli, S.L. Yong, M. Gori, M. Hagenbuchner, A.C. Tsoi, and M. Maggini. Graph Neural Networks for ranking web pages. In Proceedings of the 2005 IEEE/WIC/ACM Conference on Web Intelligence, WI2005, pages 666-672, Washington, DC, USA, 2005. IEEE Computer Society.
  9. S.L. Yong, M. Hagenbuchner, F. Scarselli, A. C. Tsoi, and M. Gori. Document mining using Graph Neural Networks. In Norbert Fuhr, Mounia Lalmas, and Andrew Trotman, editors, Proceedings of the 5th International Workshop of the Initiative for the Evaluation of XML Retrieval, INEX 2006, Revised and Selected Papers, volume 4518 of Lecture Notes in Computer Science, pages 458-472. Springer, 2006.