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Title: Fuzzy classification with distance-based prototypes Authors:  Itziar Irigoien - University Basque Country (Spain) [presenting]
Concepcion Arenas - University of Barcelona (Spain)
Abstract: Supervised or unsupervised classification of objects are important areas of research and needed in practical applications in a variety of fields such as environmental sciences, medicine, economy and psychology. Distance-based approaches offer a complementary perspective to classical units$\times$variables techniques. Besides fuzzy approaches bring the opportunity to handle situations where there is not a clear-cut relationship between units and where units present different degrees of membership. The aim is to combine both aspects and introduce a novel Fuzzy Classification method. To that end, first, fuzzy versions of distance-based concepts such as geometric variability, proximity function, distance between classes and depth function are extended. Then, inspired by previous works, a fuzzy classification methodology is proposed including the aforementioned distance-based perspective. The proposed methodology covers supervised and non-supervised tasks and in contrast with more classical approaches, offers characteristic prototypes of a given data set instead of centroids. To show its effectiveness, the proposed approach was compared with Supervised Fuzzy Partitioning on some classical datasets as well as simulated datasets. Finally, the results we obtained on real datasets are reported showing the good performance of the new methodology.