Fair Method for Spectral Clustering to Improve Intra-cluster Fairness

Recently, the fairness of the algorithm has aroused extensive discussion in the machine learning community.Given the widespread popularity of spectral clustering in modern data science, studying the algorithm fairness of spectral clustering is a crucial topic.Existing fair spectral clustering algorithms have two shortcomings: 1) poor fairness performance; 2) work only for single sensitive attribute.In this paper, the fair spectral clustering problem is regarded as a constrained spectral clustering problem.By solving the feasible solution set of constrained spectral clustering, an unnormalized fair spectral clustering（UFSC） method is proposed to improve fairness performance.In addition, the paper also proposes a fair clustering algorithm suitable for multiple sensitive attribute constraints.Experimental results on multiple real-world datasets demonstrate that the UFSC and MFSC are fairer than the existing fair spectral clustering algorithms.