Centroid Ratio for a Pairwise Random Swap Clustering Algorithm

Abstract

Clustering algorithm and cluster validity are two highly correlated parts in cluster analysis. In this paper, a novel idea for cluster validity and a clustering algorithm based on the validity index are introduced. A Centroid Ratio is firstly introduced to compare two clustering results. This centroid ratio is then used in prototype-based clustering by introducing a Pairwise Random Swap clustering algorithm to avoid the local optimum problem of $k$ -means. The swap strategy in the algorithm alternates between simple perturbation to the solution and convergence toward the nearest optimum by $k$ -means. The centroid ratio is shown to be highly correlated to the mean square error (MSE) and other external indices. Moreover, it is fast and simple to calculate. An empirical study of several different datasets indicates that the proposed algorithm works more efficiently than Random Swap , Deterministic Random Swap , Repeated k-means or k-means++ . The algorithm is successfully applied to document clustering and color image quantization as well.