Self-updating clustering algorithm for estimating the parameters in mixtures of von Mises distributions

Abstract

The EM algorithm is the standard method for estimating the parameters in finite mixture models. Yang and Pan [25] proposed a generalized classification maximum likelihood procedure, called the fuzzy c-directions (FCD) clustering algorithm, for estimating the parameters in mixtures of von Mises distributions. Two main drawbacks of the EM algorithm are its slow convergence and the dependence of the solution on the initial value used. The choice of initial values is of great importance in the algorithm-based literature as it can heavily influence the speed of convergence of the algorithm and its ability to locate the global maximum. On the other hand, the algorithmic frameworks of EM and FCD are closely related. Therefore, the drawbacks of FCD are the same as those of the EM algorithm. To resolve these problems, this paper proposes another clustering algorithm, which can self-organize local optimal cluster numbers without using cluster validity functions. These numerical results clearly indicate that the proposed algorithm is superior in performance of EM and FCD algorithms. Finally, we apply the proposed algorithm to two real data sets.

Keywords:

• circular data
• mixtures of von Mises distributions
• robust
• self-updating process

Acknowledgements

The authors thank the anonymous reviewers for their constructive comments to improve the presentation of the paper. This work was supported in part by the National Science Council of the Republic of China under Grant NSC 99-2118-M-134-001.