Keynote: Diffusion Learning Machines
Marco Gori
Most of nowadays learning schemes neglect 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 talk, I propose to represent the data by graphs where the nodes contains real vectors so as to provide a structural representation of each pattern, and to adopt the same formalism for expressing data relationships. I introduce a new model, called diffusion learning machine (DLM), whose decision mechanism relies on a diffusion information process through the whole graphical domain more than on the classic target prediction that associates values to single examples. I give conditions under which the proposed model turn out to be a globally stable dynamical system which returns a unique value on the nodes of the graphical domain. Moreover, I prove that the function on the nodes that is returned is continuously differentiable with respect to the learning parameters, which makes it possible to use the tradition optimization framework for learning and derive an efficient neural-like gradient computational scheme. Depending on the choice of the mechanism to implement the diffusion process, DLMs turn out to generalize recursive neural networks as well as classic diffusion models described by the Laplacian of the graph. Interestingly, apart from cases of special symmetries, the strong dynamical restrictions to yield stability do not limit the computational power of DLMs, since I prove that DLM exhibits a universal approximation property in graphical domains. I report very promising experimental results for problems taken from graph matching, bioinformatics, and Web link analysis.