The structural clustering and analysis of metric based on granular space

摘要

In this paper, the research on granular space theory and structural clusters of metric based on granular space is introduced, and a comprehensive of theoretical and analyzing methodologies is developed. The granular space theory is established based on normalized equicrural metric, and the consistent cluster characteristics of ordered granular spaces are derived. Details are shared for some related subject, such as the granular representation of structural cluster from normalized metric, the optimal cluster determination, the fusion of structural cluster, and the structural clustering analysis of metric space based on granular space, etc. Theories and methodologies are established for structural clustering based on metric space, and developed a series of mathematical models and formal description tools for the research on its potential applications. Direct and geometric interpretations for structural clustering analysis are provided to assist deeper understanding the essence of clustering (or classifying) procedure.