Information granulation: a search for data structures

Revealing a structure in data is of paramount importance in a broad range of problems of information processing. In spite of the specificity of the problem in which such analysis is realized, there is an evident commonality of all these pursuits worth emphasizing. One can distinguish between a core and a residual of the data structure. In this study, we propose a formal environment supporting these concepts and develop its algorithmic fabric. The algorithms leading to the development of information granules lend themselves to the Fuzzy C-Means (FCM) equipped with the Tchebyschev (1<sub>∞</sub>) metric. The paper offers a novel contribution of a gradient-based learning of the prototypes developed in this form of clustering. The 1<sub>∞</sub> metric promotes a design of easily interpretable hyperboxes. In this setting, we quantify the notion of the core and residual part of the data. An interaction between information granules is discussed as well