Graph-Based Soft-Balanced Fuzzy Clustering

Spectral clustering have attracted more and more attention due to their well-defined mathematical frameworks and superior performance. However, there still exist two limitations to be solved: 1) most spectral clustering methods consist of two independent stages, which may cause unpredictable deviation of obtained clustering results from the genuine ones and lead to severe information loss and performance degradation; 2) spectral clustering methods employ the hard clustering mode, which lacks interpretability for data points in the boundary area belonging to multiple clusters. To simultaneously address these challenging issues for spectral clustering, we propose a graph-based soft-balanced fuzzy clustering (GBFC) model. Specifically, we explicitly preserve the nonnegative property of the clustering indicator matrix to enhance the interpretability of clustering results. Moreover, row normalization is imposed on the cluster indicator matrix to show the membership of each data point to different clusters. Additionally, a novel balanced constraint is designed to regularize the clustering results and constrain the size of clusters. We can directly obtain the clustering assignments without any post-processing, and the limitations of the previous two-stage clustering framework can be effectively addressed. Extensive experiments performed on both synthetic datasets and real world datasets demonstrate the superiority and effectiveness of the proposed algorithm compared with several state-of-the-art methods.