A Method for Initializing the K-means Clustering Algorithm Using Delaunay Triangulation

Abstract

The traditional k-means algorithm has been widely used as a simple and efficient clustering method. However, the algorithm often converges to local minima for the reason that it is sensitive to the initial cluster centers. In this paper, a novel algorithm for selecting initial cluster centers on the basis of Delaunay Triangulation (DT) is proposed. We first define the representative data points and their corresponding densities. Furthermore, a novel distance measure between the representative data points with consideration of density and Euclidean distance is presented. Finally, DT-based initialization method for the k-means algorithm is proposed. The time complexity of the proposed algorithm is also analyzed. The proposed algorithm is applied to five data sets with different dimensions to compute the initial cluster centers for the k-means algorithm. Compared with CCIA, kd-tree and k-means++, the proposed algorithm demonstrates superior clustering performance in obtaining the initial cluster centers for the k-means algorithm.