Fuzzy clustering algorithm with locality preserving based on anchor graph

Fuzzy clustering, as an important data analysis method, has gained extensive application in several fields. However, there are two problems with traditional fuzzy clustering that affect the performance of clustering results. One problem is that traditional fuzzy clustering algorithms map samples to membership space, only considering the relationship between samples and cluster centers, without taking into account local structural information between samples. Another problem is that traditional fuzzy clustering algorithms fail to take into account both the balance and distinguishability of membership degrees simultaneously. To address these problems, we propose a fuzzy clustering algorithm with locality preserving based on anchor graph (FCLPAG). We utilize the graph regularization term to ensure that the samples in the membership space preserve the local structure in the original space. To expedite the clustering, the model first constructs the membership matrix A from samples to anchors, then learns the membership matrix B from anchors to cluster centers, and finally obtains the membership matrix U from samples to cluster centers by U=AB. In addition, we introduce a quadratic programming term and a cluster balance constraint term to ensure that the clustering results are simultaneously distinguishable and balanced. Finally, we used an iterative optimization method to address the model, and conducted experiments on eight benchmark datasets, which demonstrated the effectiveness of the proposed algorithm.