Three Fuzzy c-Shapes Clustering Algorithms for Series Data

Various fuzzy clustering algorithms have been proposed for vectorial data. However, most of these methods have not been applied to series data. This study presents three fuzzy clustering algorithms for series data based on shape-based distances. The first algorithm involves Shannon entropy regularization of the k-shape objective function. The second algorithm is similar to the revised Bezdek-type fuzzy c -means algorithm obtained by replacing the membership of the hard c -means objective function with its power. The third algorithm involves Tsallis entropy regularization of the objective function of the second algorithm. Theoretical observations revealed that the third algorithm is a generalization of the first and second algorithms, which was validated by numerical experiments. Furthermore, numerical experiments were performed using 11 benchmark datasets to demonstrate that the third algorithm outperforms the others in terms of accuracy.