Robust fuzzy relational clustering of non-linear data

In many practical situations data may be characterized by non-linear structures. Classical (hard or fuzzy) algorithms, usually based on the Euclidean distance, implicitly lead to spherical shape clusters and, therefore, do not identify clusters properly. In this paper we deal with non-linear structures in clustering by means of the geodesic distance, able to capture and preserve the intrinsic geometry of the data. We introduce a new fuzzy relational clustering algorithm based on the geodesic distance. Furthermore, to improve its adequacy, a robust version is proposed in order to take into account the presence of outliers.