Clustering: A Rough Set Approach to Constructing Information Granules

This article introduces an approach to constructing clusters based on rough set theory. An algorithm for finding clusters of sample sensor signal values is introduced using a measure of closeness of information granules and a distance metric defined relative to a partition of the universe into equivalence classes containing elements that are considered indistinguishable from each other. The elements of each equivalence class are associated with what is known as a cell (or box) of a δ-mesh. The idea of an indistinguishability relation is briefly presented. It is this indistinguishability relation that underlies the construction each δ-mesh. Closeness of information granules is determined by measuring the separation between cells in a δ-mesh. The “center” of every cluster is a cell in a δ-mesh that is found using a measure of maximal rough inclusion. A cluster is constructed by starting with a particular cell in a δ-mesh and then gathering in all elements along the borders of the center and neighboring cells in the δ-mesh. The harvest of clusters continues until all non-empty cells in a δ-mesh have been considered. The problem of discovering clusters themselves as well as the size of a population clusters has been motivated by recent studies of rough neural networks and the classification of sensor signals. A sensor signal is a non-empty, finite, temporally ordered set of sample sensor signal values. Classification of sensor signals requires measurements of sample signal values over subintervals of time. The contribution of this article is the introduction of a rough set approach to constructing clusters.