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Fuzzy Clustering Analysis is one of the most popular research currently. It attracts people's attention for it's validity in resolving fuzzy problem. With the development of computer science, Fuzzy Clustering Analysis based on objective function became hot topics and Fuzzy C-means Clustering Algorithm is one of the most perfect and most widely used theories although there are some drawbacks for the classical algorithm itself. This paper summarizes the progress of FCM algorithm, and some algorithm improvements were analyzed and compared.