Neural Networks for Complex Data

KI - Künstliche Intelligenz manuscript No. (will be inserted by the editor) Abstract Artificial neural networks are simple and efficient machine learning tools. Defined originally in the traditional setting of simple vector data, neural network models have evolved to address more and more difficulties of complex real world problems, ranging from time evolving data to sophisticated data structures such as graphs and functions. This paper summarizes advances on those themes from the last decade, with a focus on results obtained by members of the SAMM team of Université Paris 1. 1 Introduction In many real world applications of machine learning and related techniques, the raw data are not anymore in a standard and simple tabular format in which each object is described by a common and fixed set of numerical attributes. This standard vector model, while useful and efficient, has some obvious limitations: it is limited to numerical attributes, it cannot handle objects with non uniform descriptions (e.g., situations in which some objects have a richer description than others), relations between objects (e.g., persons involved in a social network), etc. In addition, it is quite common for real world applications to have some dynamic aspect in the sense that the data under study are the results of a temporal process. Then, the traditional hypothesis of statistical independence between observations does not hold anymore: new hypothesis and theoretical analysis are needed to justify the mathematical soundness of the machine learning methods in this context.