Granular Prototyping in Fuzzy Clustering
A Bargielaa, Witold Pedryczb c, Kaoru Hirotad
- aDepartment of Computing and Mathematics, Nottingham Trent University, Nottingham, UK
- bDepartment of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada
- cSystems Research Institute, Polish Academy of Sciences, Warsaw, Poland
- dDepartment of Computational Intelligence and Systems Science, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, Yokohama, Japan
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Abstract
We introduce a logic-driven clustering in which prototypes are formed and evaluated in a sequential manner. The way of revealing a structure in data is realized by maximizing a certain performance index (objective function) that takes into consideration an overall level of matching (to be maximized) and a similarity level between the prototypes (the component to be minimized). The prototypes identified in the process come with the optimal weight vector that serves to indicate the significance of the individual features (coordinates) in the data grouping represented by the prototype. Since the topologies of these groupings are in general quite diverse the optimal weight vectors are reflecting the anisotropy of the feature space, i.e., they show some local ranking of features in the data space. Having found the prototypes we consider an inverse similarity problem and show how the relevance of the prototypes translates into their granularity.