A Fuzzy Clustering Approach Using Reward and Penalty Functions

In this study, the objective function of the most used fuzzy c-means algorithm is reformulated based on two reward and penalty functions. The reward function is defined as the original data in a given dataset, but the penalty function is characterized by a group of additional data in terms of the original data distributions. These additional data are distributed around each group of aggregating original data, and their effects are to enlarge the values of the objective function against the tendency that the determined clustering centers tend these data. Consequently, the fuzzy clustering based on this reformulated objective function achieves two merits: higher accuracy and less time cost. Moreover, after using the two reward and penalty functions, we found that the estimation of the real number of clusters based on a partitioning coefficient function are more accurate than its origin in most datasets. Four successful experiments are present to verify the usefulness of our approach.