Similarity-based Neuro-Fuzzy Networks and Genetic Algorithms in Time Series Models Discovery*

This paper presents a hybrid soft computing technique for the study of time varying processes based on a combination of neurofuzzy techniques with evolutionary algorithms, in particular, genetic algorithms . Two problems are simultaneously addressed: the discovery of patterns of dependency in general multivariate dynamic systems (in an optimal or quasi-optimal sense), and the construction of a suitable initial representation for the function expressing the dependencies for the best model found. The patterns of dependency are represented by general autoregresive models (not necessarily linear), relating future values of a target variable with its past values as well as with those of the other observed variables. These patterns of dependencies are explored with genetic algorithm, whereas the functional approximation is constructed with a neurofuzzy heterogeneous network. The particular kind of neurofuzzy network chosen uses a nonclassical neuron model based on similarity in the hidden layer, and a classical neuron model in the output layer. An instance-based training approach allows a rapid construction of a complete network from the multivariate signal set and the dependency pattern under exploration, thus allowing the investigation of many prospective patterns in a short time. The main goal of the technique is the rapid prototyping and characterization of interesting or relevant interdependencies, especially in poorly known complex multivariate processes. The genetic search of the space of possible models (astronomically huge in most practical problems) doesn’t guarantee the optimality of the models discovered. However, it provides a set of plausible dependency patterns explaining the interactions taking place, which can be refined later on by using more sophisticated techniques (also more time consuming) as function approximators, to improve the quality of the forecasting operator. Examples with known time series show that the proposed approach gives better results than the classical statistical one.