Fuzzy c-means clustering algorithm for directional data (FCM4DD)

• A new approximation for clustering of directional data is proposed.
• The proposed method is simple, fast and stable when compared to other methods.
• The proposed method can be used for N-dimensional directional data.
• Tradition validation index methods can be used with proposed method.

Cluster analysis is a useful tool used commonly in data analysis. The purpose of cluster analysis is to separate data sets into subsets according to their similarities and dissimilarities. In this paper, the fuzzy c-means algorithm was adapted for directional data. In the literature, several methods have been used for the clustering of directional data. Due to the use of trigonometric functions in these methods, clustering is performed by approximate distances. As opposed to other methods, the FCM4DD uses angular difference as the similarity measure. Therefore, the proposed algorithm is a more consistent clustering algorithm than others. The main benefit of FCM4DD is that the proposed method is effectively a distribution-free approach to clustering for directional data. It can be used for N-dimensional data as well as circular data. In addition to this, the importance of the proposed method is that it would be applicable for decision making process, rule-based expert systems and prediction problems. In this study, some existing clustering algorithms and the FCM4DD algorithm were applied to various artificial and real data, and their results were compared. As a result, these comparisons show the superiority of the FCM4DD algorithm in terms of consistency, accuracy and computational time. Fuzzy clustering algorithms for directional data (FCM4DD and FCD) were compared according to membership values and the FCM4DD algorithm obtained more acceptable results than the FCD algorithm.