Studies On New Fuzzy Clustering Algorithms And Clustering Validity Problems

Fuzzy clustering analysis is an important branch of fuzzy pattern recognition, it is an unsupervised pattern recognition method, and was widely used in many fields. The paper ntains mainly two parts. Firsts, the traditional fuzzy c-means clustering algorithm is studied and the meaning of the membership degrees in fuzzy c-means clustering is discussed again; some c-means clustering algorithms are proposed for interval-values data sets; weighted fuzzy c-means clustering algorithm is proposed to overcome the shortcomings of fuzzy c-means clustering algorithm. Seconds. the clustering validity problems are studied, two type抯 functions are proposed which based on the fuzzy partitions and the geometry structures of data set. Finally, some commonly used threshold image segmentation methods are explained by the view of mathematics. This dissertation is classified into six chapters: In Chapter 1, clustering analysis is stated, a brief review of the development and meaning of fuzzy clustering algorithms and clustering validity problems are surveyed. the main achievements and arrangements of the paper are given. In Chapter 2, hard c-means clustering algorithm and fuzzy c-means clustering algorithm are simply stated, the meaning of the membership degrees in fuzzy c- means clustering is discussed again; some clustering algorithms are proposed for interval-values data sets. In Chapter 3, weighted fuzzy c-means clustering algorithm and weighted hard c- means clustering algorithm are proposed. the convergence of the weighted fuzzy c- means clustering algorithm is discussed. In Chapter 4, three clustering validity functions are proposed based on the partitions of data set. They used the concepts of possibilistic distribution, Shannon entropy and subsethood measure. In Chapter 5, two clustering validity functions are proposed based on the geometry structures of data set. They used the concepts of frizzy relation degree between classes and fuzzy Fisher distance between classes. In Chapter 6, the Otsu's thresholding image segmentation method is explained again by weighted hard c-means clustering, the minimum error thresholding method based on Gauss distribution is explained by relative entropy and the minimum error thresholding method based on Poisson distribution is explained by relative entropy and maximum relationship principle.