From clustering to granular clustering: A granular representation of data in pattern recognition and system modeling

Fuzzy clustering has been one of the commonly used vehicles to construct information granules (whose description is provided in terms of prototypes and partition matrices). The quality of resulting information granules can be assessed by quantifying how well the original numeric data from which information granules have been constructed can be represented (granulated) by information granules and subsequently reconstructed (degranulated). We recall the concept of the reconstruction process and show how the inevitable reconstruction errors can be handled (and reduced) by granular generalizations of the representatives of fuzzy clusters, namely granular propototypes (hyperboxes) and granular (interval-valued) partition matrices. Their construction is presented in detail, several ways of reconstruction are discussed and an optimization problem of the level of information granularity involved is raised.