Fuzzy c-ordered-means clustering

Abstract

Fuzzy clustering helps to find natural vague boundaries in data. The fuzzy c-means method is one of the most popular clustering methods based on minimization of a criterion function. However, one of the greatest disadvantages of this method is its sensitivity to the presence of noise and outliers in data. This paper introduces a new robust fuzzy clustering method named Fuzzy C-Ordered-Means (FCOM) clustering. This method uses both the Huber's M-estimators and the Yager's OWA operators to obtain its robustness. The proposed method is compared to many other ones, e.g.: the Fuzzy C-Means (FCM), the Possibilistic Clustering (PC), the fuzzy Noise Clustering Method (NCM), the Lp norm clustering (Lp FCM) (0<p<1), the L1 norm clustering (L1 FCM), the Fuzzy Clustering with Polynomial Fuzzifier (PFCM) and the ε-insensitive Fuzzy C-Means (βFCM). To this end experiments on synthetic data with outliers have been performed as well as on data with heavy-tailed and overlapping groups of points in background noise.