Title: Distances for clustering non-precise information: A comparative study
Authors: Ana Belen Ramos-Guajardo - University of Oviedo (Spain) [presenting]
Maria Brigida Ferraro - Sapienza University of Rome (Italy)
Abstract: Different clustering methods for non-precise information have been developed in the recent decades. Some of those methods include also fuzziness in the process. This is the case of the well-known fuzzy k-means procedure for clustering fuzzy numbers. The distance between fuzzy numbers employed is basically defined as a weighted sum of the squared Euclidean distances between their mid-points and their spreads. Nevertheless, the fuzzy k-means approach does not allow for the correlation structure between variables, which is a shortcoming whenever the shape of the clusters is not spherical. For this reason, the Mahalanobis distance involving the corresponding covariance matrices between the variables has been introduced, and a fuzzy clustering approach based on that distance is proposed. Both methodologies are compared by means of simulation studies, and a real-life situation is also tackled.