Representation of Granularity for Non-Euclidian Relational Data by Jaccard Coefficients and Binary Classifications

Abstract

In this paper we present a method for representing the granularity for asymmetric, non-Euclidean relational data. It firstly builds a set of binary classifications based on the directional similarity from each object. After that, the strength of discrimination knowledge is quantified as the indiscernibility of objects based on the Jaccard similarity coefficients between the classifications. Fine but weak discrimination knowledge supported by the small number of binary classifications is more likely to be coarsened than those supported by the large number of classifications, and coarsening of discrimination knowledge causes the merging of objects. Accoding to this feature, we represent the hierarchical structure of data granules by a dendrogram generated by applying the complete-linkage hierarchical grouping method to the derived indiscernibility. This enables users to change the coarseness of discrimination knowledge and thus to control the size of granules.