Fuzzy Clustering Optimal k Selection Method Based on Multi-objective Optimization

Abstract Because of the complexity of data sets from the real world, it is difficult to classify the data sets clearly and effectively, thus we prefer to adopt fuzzy clustering approaches to analyze the data sets. However, due to the variety of fuzzy clustering algorithms, and the different number of clusters will lead to different clustering results. The number of clusters is closely related to the clustering division, so how to determine the number of fuzzy clustering (k ) has become a problem. Until now, many researchers have proposed utilizing fuzzy clustering validity indexes to deal with this kind of problem. However, the effectiveness index of fuzzy clustering can only be evaluated on the basis of the fuzzy clustering algorithm FCM to divide the clusters. When the range of k value is too large, FCM's clustering for different k values is quite time-consuming. From this perspective, this paper proposes a fuzzy clustering optimal k selection method based on multi-objective optimization (FMOEA-K). Different from the traditional methods, this method combines the fuzzy clustering effectiveness index with multi-objective optimization algorithm (MOEA), and uses multi-objective optimization algorithm to search the appropriate cluster center concurrently. Because of the concurrency of the multi-objective optimization algorithm, the calculation time is shortened. The experimental results show that compared with the traditional method, the FMOEA-K can shorten the calculation time and improve the accuracy of calculating the optimal k value.