A Novel Cluster Validity Index Based on Local Cores

It is critical to evaluate the quality of clusters for most cluster analysis. A number of cluster validity indexes have been proposed, such as the Silhouette and Davies-Bouldin indexes. However, these validity indexes cannot be used to process clusters with arbitrary shapes. Some researchers employ graph-based distance to cluster nonspherical data sets, but the computation of graph-based distances between all pairs of points in a data set is time-consuming. A potential solution is to select some representative points. Inspired by this idea, we propose a novel Local Cores-based Cluster Validity (LCCV) index to improve the performance of Silhouette index. Local cores, with local maximum density, are selected as representative points. Since graph-based distance is used to evaluate the dissimilarity between local cores, the LCCV index is effective for obtaining the optimal cluster number for data sets containing clusters with arbitrary shapes. Moreover, a hierarchical clustering algorithm based on the LCCV index is proposed. The experimental results on synthetic and real data sets indicate that the new index outperforms existing ones.