A Comparison Between External and Internal Cluster Validity Indices

Abstract

This paper presents a comparison between external and internal cluster validity indices with a similar bounded index range. F-measure (FM) and Fowlkes-Mallows (FMI) of external validity indices, as well as Silhouette (SIL) of internal validity index, were chosen for this comparative analysis. Ten numerical data sets, namely Haberman, BUPA (liver disorder), Wisconsin Diagnostic Breast Cancer (WDBC), Iris, Seeds, Wine, User Knowledge, Cleveland, Segmentation, and Glass, were deployed to benchmark the clustering outcomes based on Fuzzy C-Mean (FCM) algorithm. Mean, minimum, and maximum scores were calculated to determine the similarities and differences among the indices. Pearson correlation was reported as well. As a result, the index scores displayed a slight difference between the external and internal validity indices. A moderate and positive correlation was noted between the external and internal validity index (r=. 66, r=.65 p<0.01) scores. This correlation signifies a similar graph pattern between the cluster validity indices. This comparative analysis revealed that the external and internal cluster validity indices with similar bounded index ranges and slightly different index scores generate a moderate and positive correlation with a similar graph pattern.