
Logo Recognition by Recursive Neural Networks
P. Frasconi ? E. Francesconi ? M. Gori?
S. Marinai ? J.Q. Sheng ? G. Soda ? A. Sperduti ffl
? Dipartimento di Sistemi e Informatica  Universit?a di Firenze  Italy
? Dipartimento di Ingegneria dell'Informazione  Universit?a di Siena  Italy
ffl Dipartimento di Informatica  Universit?a di Pisa  Italy
The adaptive computational scheme of statistical models and artificial neural networks is very wellsuited for pattern recognition. It is commonly recognized, however, that these adaptive models, and especially neural networks, can hardly deal with highlystructured information. On the other hand, most of the models proposed in the field of syntactic pattern recognition are verywell suited for incorporating pattern grammatical regularities but, one of their drawbacks is that they are not strongly oriented to face the presence of noise. This scenario seems to be mainly due to the development of computational approaches that are basically oriented to either dealing with symbols or with unstructured information, whilst in the field of pattern recognition one is often looking for a balanced combination of the symbolic and subsymbolic processing levels.
In order to fill the gap from symbolic and subsymbolic processing, instead of processing vector of reals, some researchers have recently investigated the feasibility of learning from examples structured data by using recursive artificial neural networks (RANNs) [1]. The basic entity that RANNs are able to adaptively processing is a data structure, mathematically described by a directed ordered acyclic graph (DOAG) with labeled nodes. Each node v in the DOAG is labeled with a variable Uv, which we shall assume to be continuous and multivariate. It is required that the DOAG possess a supersource, i.e., a vertex s 2 V such that every vertex in V can be reached by a path starting from s. A simple class which satisfies the above conditions is the class of linear chains, in which nodes v are associated to a serial order on the labels (i.e. v effectively corresponds to a discrete time index). In fact, recurrent neural networks can be thought of as a special case of recursive ANNs that deal with linear chains. RANNs are a particular class of models operating structural transductions. In a general formulation, a structural transduction is based on the following recursive state space representation:
Xv = f(Xch(v); Uv) (1)
where Xv is a multivariate continuous state variable associated to the generic node v, ch(v) denotes the ordered set of children of v, and f is a generalized state transition function. Computation proceeds following the reverse topological sort of the input data structure U . In order to apply the above equation it is also necessary to specify the state associated to the base step of recursion. This is analogous to the concept of initial state X0 in classic dynamical systems (such as recurrent neural networks) that deal with sequentially ordered data. In the case of DOAGs it is necessary to specify a set of frontier states, which