Mining Cellular Automata DataBases throug PCA Models

Abstract

Cellular Automata are discrete dynamical systems that evolve following simple and local rules. Despite of its local simplicity, knowledge discovery in CA is a NP problem. This is the main motivation for using data mining techniques for CA study. The Principal Component Analysis (PCA) is a useful tool for data mining because it provides a compact and optimal description of data sets. Such feature have been explored to compute the best subspace which maximizes the projection of the I/O patterns of CA onto the principal axis. The stability of the principal components against the input patterns is the main result of this approach. In this paper we perform such analysis but in the presence of noise which randomly reverses the CA output values with probability $p$. As expected, the number of principal components increases when the pattern size is increased. However, it seems to remain stable when the pattern size is unchanged but the noise intensity gets larger. We describe our experiments and point out further works using KL transform theory and parameter sensitivity analysis.