A K-means Clustering Approach Based on Grey Theory

Abstract

A lot of clustering algorithms based on grey system theory, especially based on the grey relational matrix, have been already reported, which finds out a centroid of each class by moving given objects as vectors. We developed new clustering procedure called grey K-means, which is able to handle the number of required clusters such as the hard K-means or the fuzzy c-means. Assume that the number of found clusters by the proposal is between 1 and the number of classified instances, a required threshold value is exist in [0,1]. We defined a value range of the threshold as the interval grey number, and the range is specified automatically until obtaining the required clusters. In addition a new clustering method which analyzes the grey relational matrix closely instead of moving vectors is suggested. Several well-known data sets in the classification problem are applied, and we discuss their performances and the optimal threshold value.