A fast method for fuzzy neural modeling and refinement

In the identification of complex dynamic systems using fuzzy neural networks, one of the main issues is the curse of dimensionality, which makes it difficult to retain a large number of system inputs or to consider a large number of fuzzy sets. Moreover, due to the correlations, not all possible network inputs or regression vectors in the network are necessary and adding them simply increases the model complexity and deteriorates the network generalisation performance. In this paper, the problem is solved by first proposing a fast algorithm for selection of network terms, and then introducing a refinement procedure to tackle the correlation issue. Simulation results show the efficacy of the method.

Exploratory analysis of spatiotemporal patterns of cellular automata by clustering compressibility

In this paper we study the classification of spatiotemporal pattern of one-dimensional cellular automata (CA) whereas the classification comprises CA rules including their initial conditions. We propose an exploratory analysis method based on the normalized compression distance (NCD) of spatiotemporal patterns which is used as dissimilarity measure for a hierarchical clustering. Our approach is different with respect to the following points. First, the classification of spatiotemporal pattern is comparative because the NCD evaluates explicitly the difference of compressibility among two objects, e.g., strings corresponding to spatiotemporal patterns. This is in contrast to all other measures applied so far in a similar context because they are essentially univariate. Second, Kolmogorov complexity, which underlies the NCD, was used in the classification of CA with respect to their spatiotemporal pattern. Third, our method is semiautomatic allowing us to investigate hundreds or thousands of CA rules or initial conditions simultaneously to gain insights into their organizational structure. Our numerical results are not only plausible confirming previous classification attempts but also shed light on the intricate influence of random initial conditions on the classification results.