Title: Generalization of the Mahalanobis distance for star-shaped sets: An application to fuzzy clustering Authors:  Ana Belen Ramos-Guajardo - Fundacion Universidad de Oviedo (Spain) [presenting]
Maria Brigida Ferraro - Sapienza University of Rome (Italy)
Gil Gonzalez-Rodriguez - University of Oviedo (Spain)
Abstract: Several clustering techniques for imprecise information have emerged over the past few decades. Some of these methods incorporate fuzziness into the clustering process, such as the widely recognized fuzzy k-means algorithm. This algorithm has also been previously developed to handle the clustering of star-shaped sets. However, the fuzzy k-means method has a limitation: it does not account for the correlation structure between variables, which becomes problematic when the clusters are not spherical in shape. To overcome this drawback, the Mahalanobis distance, wich considers covariance matrices between variables, has been introduced. Thus, a novel fuzzy clustering algorithm for star-shaped sets based on the Mahalanobis distance is proposed. The performance of both the fuzzy k-means method and the proposed approach is evaluated through a real-world application.