Fuzzy clustering with evolutionary algorithms

Objective function based fuzzy clustering aims at nding a fuzzy partition by optimizing a function evaluating a (fuzzy) assignment of a given data set to clusters, that are characterized by a set of parameters, the so{called prototypes. The iterative optimization technique usually requires the objective function not only to be diierentiable, but prefers also an analytical solution for the equations of necessary conditions for local optima. Evolutionary algorithms are known to be an alternative robust optimization technique which are applicable to quite general forms of objective functions. We investigate the possibility of making use of evolutionary algorithms in fuzzy clustering. Our experiments and theoretical investigations show that the application of evolutionary algorithms to shell clustering, where the clusters are in the form of geometric contours, is not very promising due to the shape of the objective function, whereas they can be helpful in nding solid clusters that are not smooth, for example rectangles or cubes. These types of clusters play an important role for fuzzy rule extraction from data.