A comparison of validity indices on fuzzy C-means clustering algorithm for directional data

摘要

The FCM4DD fuzzy directional clustering algorithm, a simple, consistent and reliable method, requires the user to predefine the number of clusters. The determination of the number of clusters is very important in an unsupervised clustering algorithm. The number of clusters of directional data can be determined by observing scatter plots which are drawn in a one- or two-dimensional space. However, if the size of the data is large and multi-dimensional, the determination of the number of clusters is very difficult. In this study, the determination of the optimal number of clusters is aided by the parameters which are calculated by the FCM4DD clustering algorithm. The partition coefficient and the partition entropy validity indices use only the fuzzy membership degrees. Therefore, these validity indices do not require any changes in order to be adapted to directional data. However, the Fukuyama-Sugeno, the Xie-Beni and the Pakhira-Bandyopadhyay-Maulik indexes were adapted to directional data by using the angular difference.