Granular Data Description: Designing Ellipsoidal Information Granules

Granular computing (GrC) has emerged as a unified conceptual and processing framework. Information granules are fundamental constructs that permeate concepts and models of GrC. This paper is concerned with a design of a collection of meaningful, easily interpretable ellipsoidal information granules with the use of the principle of justifiable granularity by taking into consideration reconstruction abilities of the designed information granules. The principle of justifiable granularity supports designing of information granules based on numeric or granular evidence, and aims to achieve a compromise between justifiability and specificity of the information granules to be constructed. A two-stage development strategy behind the construction of justifiable information granules is considered. First, a collection of numeric prototypes is determined with the use of fuzzy clustering. Second, the lengths of the semi-axes of ellipsoidal information granules to be formed around such prototypes are optimized. Two optimization criteria are introduced and studied. Experimental studies involving synthetic data set and data sets coming from the machine learning repository are reported.