Adaptive processing of data structures

Many artificial and natural systems are often more adequately modelled using data structures, e.g., graphs, trees. For example, it is often more convenient to represent an image using data structures than by representing it using pixels. The data structure can serve as a prelude to scene analysis, image retrieval, etc. There are, broadly speaking, two ways in which data structures can be processed. One way is to consider it as generated by an underlying grammar, with defined syntax; and the other way is to consider it as an input output system, which may be modelled using neural networks. In this talk, we will discuss both approaches. We will first discuss how data structures can be modelled using an attributed grammar. Then, we will discuss the modelling of a data structure using neural networks. It is shown that both approaches are closely related. We will then derive training algorithms for the neural network models, and discuss the universal approximation properties of such models. We will demonstrate the neural network approach on a number of synthesized and practical examples.