Fuzzy C-Means Cluster Analysis Based on Mutative Scale Chaos Optimization Algorithm for the Grouping of Discontinuity Sets

An fuzzy C-means (FCM) method based on mutative scale chaos optimization algorithm (COA) is proposed for the automatic identification of discontinuity sets. The FCM method separates a data set into C clusters by minimizing the fuzzy objective function. The sine of the acute angle between discontinuity unit normal vectors is used as a measure of their distance. New cluster centers and the new value of the objective function are computed using chaotic variables iterations until the optimum cluster centers are found. To investigate the applicability of this algorithm, the cluster method was applied to an artificial data set. Owing to the ergodicity property of chaos variables, the initial chaos variables do not heavily influence the final result. Thus, the new algorithm does not need to choose the proper initial cluster centers. The validity measure indicates that the most appropriate number of sets should be three. Considering three sets, the new method is shown to perform well.