Research Of The Related Problems On Fuzzy C-Means

The research area of Fuzzy C means algorithm subordinates to Date Mining, and is one direction of Cluster Analysis, which is one kind of unsupervised algorithm based on the objective function. It is introduce the concept of fuzzy mathematical theory into the traditional cluster algorithm, and uses the membership function to represent the subordinate relation which is between the date object and cluster.The main content of the thesis are: first of all, beginning with deducing the objective function of FCM, it obtain the mathematical expressions of the membership function and cluster center in the optimal time of Cluster Analysis.Then, starting from the related problems on FCM, it discusses the theoretical basis and the specific ideas to solve the problem, and propose PFCM algorithm. The main content of the algorithm is: Firstly, since it is randomly generate the initial cluster center, the result of Cluster Analysis fluctuates according to the choice of the initial cluster center. Based on the deduced expression of the cluster center, the thesis uses data segmentation method to generate the initial cluster center in order to reduce the fluctuation. Secondly, when FCM calculates the dimensions distance of the data objects, the deviation of each dimensions maybe have a huge difference, which is likely to cover the characteristic of other dimensions. The thesis applies AHP to construct Comparison Matrix which bases on the column of the data objects and whose benchmark is the variance of the dimension characteristics, so as to calculate the weight of each dimensional feature to balance their roles. Thirdly, FCM deals with high dimensional data objects in low efficiency which is due to an iterative climbing search algorithm. In the thesis, it makes use of the idea of Polynomial Fitting method to switch the original data objects to the coefficient of multiple function which bases on the cross direction of the data objects, and then it use the coefficient to replace the each dimensional original data objects in order to enhance the efficiency of FCM. Fourthly, FCM calculates the distance of the data objects in the iterative process, hence the singular points have so large that it may greatly reduce the role of other data objects. The thesis detects the potential singular points in each iterative process, and then judges whether it is a real singular point which bases on the hypothesis testing of Variance Analysis. If it accepts the hypothesis, the singular point will be not join in the adjustment of cluster center.Finally, it performs the experiment to compare FCM with PFCM, and applies PFCM to Pattern Recognition. The experimental result and the application example demonstrate that PFCM optimize FCM at some extent and improve the performance and efficiency of FCM.