| Summary: | 博士 === 中原大學 === 應用數學研究所 === 100 === Clustering is a useful tool for data analysis. In general, there exist many different data types in data analysis where the circular data that are the directional data on the plane has been widely analyzed and used in a variety of applications. We know that the von Mises distribution is a well-known probability model for circular data. Moreover, mixtures of von Mises distributions have been popularly used as a probability model for cluster analysis on circular data. Up to date, the EM algorithm has most been as parameter estimation for mixtures of von Mises distributions and also a clustering method for circular data. In 1997, Yang and Pan also proposed the fuzzy c-directions (FCD) clustering algorithm for mixtures of von Mises distributions. However, these two algorithms are sensitive to initialization and outliers. They also need to give a cluster number a priori. In this dissertation, we propose two robust clustering algorithms for circular data that can also be as good parameter estimation methods for mixtures of von Mises distributions. One is a mean shift-based clustering method. Another one is a self-updating clustering method. The proposed algorithms are not necessary to give the number of cluster for circular data. They can automatically find a final cluster number with good clustering centers. They are also robust to initial values and outliers. Several numerical examples and comparisons with some existing clustering methods are used to demonstrate its effectiveness and superiority of these proposed methods.
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