Fair Laplace: A unified framework for fair spectral clustering

Abstract

Recent advances in fair spectral clustering algorithms have improved the fair distribution of resources during the clustering process, effectively addressing inequalities that affect certain individuals or subgroups. However, there are still drawbacks such as fewer fairness definitions and poorer fairness performance. In this paper, we provide a framework of fair spectral clustering algorithms based on fair Laplacian matrices and instantiate three fair spectral clustering algorithms under three different definitions, which include group fairness and individual fairness, as well as another type of fairness problem that exists in spectral clustering, which we define as scale fairness. We have comprehensively evaluated all three algorithms under the Fair Spectral Clustering framework, and the experimental results show that the framework has a significant effect on improving the fairness of spectral clustering. We conducted a comprehensive evaluation of three algorithms under the fair spectral clustering framework, where the largest dataset has 35,325 nodes, and we also chose to compare them with the most influential (state-of-the-art) algorithms under different fairness definitions. The experimental results show that the framework has a significant effect on improving the fairness of spectral clustering, where the maximum fairness performance is improved to 68.5%.