On robust fuzzy c-regression models

One of the most popular clustering methods based on minimization of a criterion function is the fuzzy c-means one. Its generalization by application of hyperplane shaped prototypes of the clusters is known as the Fuzzy C-Regression Models (FCRM) method. Although with this generalization many new applications of clustering emerged, it appeared to be rather sensitive to poor initialization and to the presence of noise and outliers in data. In this paper we introduce a new objective function, using the Huber's M-estimators and the Yager's OWA operators to overcome the disadvantages of the approach considered. We derive and describe an algorithm for minimization of the objective function defined. We have called it the Fuzzy C-Ordered-Regression Models (FCORM) clustering algorithm. The algorithm is compared to a few other important reference ones. To this end experiments on synthetic data with various types of noise and different numbers of outliers are carried out. We investigate the methods performance in the conditions that can be encountered in signal analysis. Large-scale simulations demonstrate the competitiveness and usefulness of the method proposed.