Ensuring Fairness in Spectral Clustering via Disparate Impact-Based Graph Construction

Abstract

Spectral clustering algorithms rely on graphs where edges are defined based on the similarity between the vertices (data points). The effectiveness and fairness of spectral clustering depend significantly on how the graph is constructed. While automated graph construction methods, which learn graphs from real-valued vector datasets, have demonstrated strong performance in the quality of clustering, fairness concerns still remain. In this work, we introduce a graph construction method that incorporates a new fairness definition—Edge Disparate Impact—into the edge relationships, aiming to produce a fair graph. This approach modifies the optimization process of automated graph construction to account for fairness, resulting in a more equitable graph. Extensive experiments were conducted to compare our method with the latest graph construction techniques and fair spectral clustering algorithms. The results prove that, by using a fair graph for spectral clustering, fairness is improved in the resulting clusters. We also demonstrate that our method outperforms baseline approaches in both fairness and the quality of clustering.