Title: A robust fuzzy clustering method for non-precise data based on trimmed regions
Authors: Ana Belen Ramos-Guajardo - University of Oviedo (Spain) [presenting]
Maria Brigida Ferraro - Sapienza University of Rome (Italy)
Abstract: The use of fuzziness in data analysis to capture the imprecision inherent in several sources of information has been deeply addressed in recent works. Additionally, various methods for clustering fuzzy data, including also fuzziness in the clustering process, have been developed in the last decades. Most of fuzzy clustering methods based on a $k-$means procedure do not take into account the influence of outliers in the data set. As an attempt to deal with this problem, a robust fuzzy clustering method is proposed based on trimming techniques, which have been shown to be very intuitive and applicable in many general spaces. The proposed methodology considers the so-called trimmed fuzzy mean and its natural empirical estimator. The trimmed fuzzy mean is defined on the basis of a generalized distance as the value minimizing the variance of a random fuzzy set (or fuzzy random variable) over the possible trimmed regions. Finally, the behaviour of the method is empirically analyzed by means of some simulation studies and its applicability is shown in a real-life example.