Fuzzy Min-Cut With Soft Balancing Effects

The clustering algorithm has always been a hot spot in machine learning, which has made great progress and been widely used in different scenarios. Due to the characteristics and requirements of some application scenarios, the branch of the balanced clustering algorithm has been developed. The ideal of these algorithms is to obtain clusters containing approximately the same number of samples. However, when there are data points distributed at the boundary of different clusters, resulting in different probabilities of their belonging, hard-partitioned balanced clustering may not be able to handle these boundary data well, thus limiting their performance. Motivated by this, we propose a Fuzzy Min-Cut with Soft Balancing Effects (FCBE) method in this article. Specifically, the FCBE model utilizes fuzzy constraints to simultaneously enhance the ability of the balanced algorithm to capture boundary data members and the advantage of directly obtaining the partitioning results of graph-cut problem without postprocessing. In addition, a sparse regularization is introduced to avoid trivial solutions and maintain the separability of the relationship matrix. Furthermore, the proposed FCBE method can be viewed as a flexibly adjustable generalization pattern that not only has clear interpretability but also can become special cases with clear physical meanings under different parameter values. The feasibility of FCBE has been verified on real datasets.