Learning fuzzy rules through ant optimization, LASSO and Dirichlet Mixtures

In the area of fuzzy systems, one of the main problems is finding the set of rules that can give us the best results in specific problems. Further, the finding of this set is a combinatorial problem. There are several techniques for building these sets, but it is possible to group them in two main classes: The bottom-up approaches and the top-down approaches. This work proposes a new top-down approach to the fuzzy systems learning based in clustering and optimization techniques. The algorithm is split in two stages: First, it determines the fuzzy sets of each input and output linguistic variable, and second, it calculates the fuzzy rules from the obtained fuzzy sets. For the first part, a Dirichlet Mixture (DM) is used to cluster data to assign a fuzzy sets to each new cluster, since a fuzzy set can be seen as a generalized probability function, and hence the fuzzy sets of a given linguistic variable can be seen as a mixture of probabilities (a Gaussian Mixture). Then, an optimization problem is solved by using Ant Colony Optimization (ACO) to generate the minimum set of possible rules for classification by using a version of the Least Absolute Shrinkage and Selection Operator(LASSO) for the fitness function. This ACO was implemented in a CUDA GPU to deal with the combinatorial problem of rule generation. Finally, this new algorithm is used to attack the problem of color image segmentation.