The Research On The Combination Of Fuzzy Clusterings And Its Application

Data analysis is an important discipline of exploring real world. Data clustering is an effective tool for data analysis. Various data clustering methods based on different theories appear in literatures. Fuzzy clustering method has been an important branch of data clustering, for it is able to discover the uncertainty existing in real world quantitatively. Literatures show that single fuzzy clustering method is often employed to partition a data set, while ensemble fuzzy clustering method does not attract much attention. By now, only Evgenia Dimitriadou et al and Gordon A. D. et al proposed a combination model of fuzzy partitions in 2002, respectively. This paper devotes to ensemble of fuzzy clusterings to push it forward.(1) This paper proposes a new method that combines multiple pairs of fuzzy cluster validity index and clustering algorithm to identify the number of clusters for the first time. Many experiments show that the proposed method is more effective and reliable than the conventional method that employs single pair of fuzzy cluster validity index and clustering algorithm to identify the number of clusters.(2) Almost all the fuzzy clustering algorithms need initial centers and they impose great impact on the fuzzy clustering. A new center initialization method based on minimum spanning tree is proposed in this paper to provide with good initial centers. Comparative experiments show that the proposed method is more effective than two current methods.(3) Different fuzzy clustering method often produces different fuzzy partitions over the same data set and no one always performs well in any cases. To solve this problem, multiple fuzzy partitions over the same data set are produced by different fuzzy clustering algorithms firstly, and then a selection model for the optimal fuzzy clustering is devised, which employs fuzzy cluster validity indexes as evaluation indexes and the classical analytic hierarchical process to comprehensively analyze each fuzzy clustering to select the optimal one from them. Many experiments show that the selected optimal fuzzy clustering is better than the others in terms of patter recognition rate.(4) Although the selection model for the optimal fuzzy clustering can successfully select the best fuzzy clustering, when all the fuzzy partitions are bad, the selected optimal one can not discover the structure of the data yet. The selection model fails in this case. To solve this problem, a cluster matching algorithm is proposed to establish the correspondence among clusters from different fuzzy partitions. Then the traditional simple majority vote, pattern recognition rate and weighted majority vote are generalized to fuzzy simple majority vote, fuzzy pattern recognition rate and fuzzy weighted majority vote. Finally, combining the cluster matching algorithm with fuzzy simple majority vote and fuzzy weighted majority vote respectively, two combination models of fuzzy partitions are proposed. Simulation experiments show that the proposed combination models can learn from the candidate fuzzy partitions'strong points to offset their weakness and combine them into a consolidate fuzzy clustering that outperforms all the candidate fuzzy partitions.(5) To further prove the feasibility of the combinatorial fuzzy clustering method, it is applied to color image segmentation and nonlinear system identification. The simulations of color image segmentation show that the combinatorial fuzzy clustering based on fuzzy weighted majority vote can learn from their strong points to offset their weakness, and produce desired color image segmentation in different cases. The methods proposed in chapter 3-5,7 are synthetically applied to the identification of the antecedent of T-S fuzzy model. Comparative experiments show that ensemble of fuzzy clusterings proposed in this paper more accurately identifies the antecedent of T-S fuzzy model and improves on the power of T-S fuzzy model to identify nonlinear systems in terms of RMES(the root of the mean of error square).