A Robust Learning Membership Scaling Fuzzy C-Means Algorithm Based on New Belief Peak

Fuzzy C-means clustering (FCM) has been a commonly used algorithm in fuzzy clustering for decades. However, it still faces two problems: how to determine the initial cluster center and how to determine the number of clusters. The recently proposed robust learning fuzzy C-means (RL-FCM) can automatically obtain the optimal number of clusters. However, it assumes that the initial cluster center is the entire dataset, which incurs a significant time cost and involves parameters that are also difficult to determine. Additionally, RL-FCM is unable to handle imbalanced datasets and datasets with a large span of sample attributes. Therefore, we propose a robust learning membership scaling fuzzy C-means algorithm based on new belief peaks (RL-MFCM). Within the framework of the confidence function, the neighbors of the sample points provide evidence for the sample points being cluster centers. Consequently, according to Jiang's combination rule, we consider the new belief peak as the initial cluster center. To avoid excessive interference of the mixing ratio of the cluster to the calculation of membership degree, we employ triangle inequality to improve the influence of the samples in the cluster in the clustering process. We analyze the time complexity of the proposed algorithm and conduct comparative experiments with existing fuzzy clustering algorithms on artificial and real datasets in the article. Experiments demonstrate that our proposed algorithm accurately estimates the number of clusters and exhibits superior clustering performance without needing initialization.