Identification Method of Correlation Dimension Scaleless Region Based on Fuzzy C-Means Clustering

The traditional calculating the correlation integral method using the large number of nested loop is time consuming. In this paper, K-D tree search method is proposed to improve the algorithm efficiency. Usually, the correlation dimension scaleless region is determined by subjective judgment, and this method will have large errors in the case of small amount of data. The new method of using fuzzy C-means clustering center membership value to identify scaleless region is proposed in this paper. Using different amount of Loren data verify the improved algorithm. Finally, results show that: K-D tree search method significantly improves the algorithm speed; using proposed method to obtain the correlation dimension values is close to the theoretical value even in the case of small amount of data; when the amount of data increases using improved algorithm to obtain the correlation dimension significantly approach the theoretical value.