Genetic Estimation of Iterated Function Systems for Accurate Fractal Modeling in Pattern Recognition Tools

In this paper, we describe an algorithm to estimate the parameters of Iterated Function System (IFS) fractal models. We use IFS to model Speech and Electroencephalographic signals and compare the results. The IFS parameters estimation is performed by means of a genetic optimization approach. We show that the estimation algorithm has a very good convergence to the global minimum. This can be successfully exploited by pattern recognition tools. However, the set-up of the genetic algorithm should be properly tuned. In this paper, besides the optimal set-up description, we describe also the best tradeoff between performance and computational complexity. To simplify the optimization problem some constraints are introduced. A comparison with sub-optimal algorithms is reported. The performance of IFS modeling of the considered signals are in accordance with known measures of the fractal dimension.