A K-MEANS Clustering Algorithm Based On ALPHA-STABLE Distribution

In the real world, there are many cases that the data follow the ALPHA-STABLE distribution. At present, the ALPHA-STABLE distribution is one of the main international research subjects. Many real-life signals could follow or be modeled by the ALPHA-STABLE distribution, so the ALPHA-STABLE distribution has been applied in more and more fields and its nature has also received better known by researchers.In this paper, the clustering of data which follows the ALPHA-STABLE distribution is highlighted. The researching on the clustering algorithm has gained a great advancement in recent years. Recently the k-means algorithm has found wide application due to its simple framework and high performance. Through study, it was concluded that the k-means algorithm is effective when clustering the gaussian data whose variance are equal, but not suitable for the ALPHA-STABLE distribution data, for this algorithm mainly utilizes data's second-order statistics. However, ALPHA-STABLE data's alpha-order (alpha is less than 2) and higher-order statistics is infinite. Thus the performance of K-Means algorithm for clustering ALPHA-STABLE distribution data is bad. For these reasons, a new clustering algorithm suitable for ALPHA-STABLE distribution data, which is based on k-means, is proposed in this paper. The conception of the new algorithm is that: Based on the Fractional Lower order Moments (FLOM) which is also called p-norm, the similarity measure was modified. The data that measured by the p-norm follow gaussian distribution. Then the k-means algorithm can be used for clustering. Now the problem that the k-means algorithm is not suitable for clustering ALPHA-STABLE data is resolved. The result of the experiment on the simulated data and real-life data shows the improvement of performance of new algorithm.