Interpretable information granules with Minkowski FCM

In this study, we investigate the interpretability of information granules that arise through the application of a Fuzzy C-Means algorithm equipped with general Minkowski metric. The paper offers a link between the classical use of Euclidean norm and the more recently reported Tchebychev norm in the context of FCM-based data granulation. In particular, we focus our attention on the topology of information granules that are derived for various alpha-cuts of the resulting fuzzy sets. We quantify deformation of the granules caused by interaction between the FCM prototypes by relating their actual shape to the ideal hyper-boxes. The analysis leads to a two level characterization of information granules: the core part that has a hyper-box shape and the residual part that has complex topology and does not convey any pattern regularity.