Equitable Representation of Demographic Groups in Constrained Spectral Clustering

Constrained spectral clustering leverages pairwise constraints, i.e., must-link and cannot-link, to guide the clustering process for given input data points. These constraints effectively align clusters by integrating external knowledge, enhancing the clustering quality. However, the resulting clusters often exhibit an unequal representation of demographic groups, such as males and females, and result in biased or unfair clusters. This imbalance not only affects the fairness of the clusters but also negatively impacts the performance of various applications that rely on equitable data representation. Although fairness has been extensively studied in spectral clustering, its integration with pairwise constraints remains largely unexplored. This paper introduces a novel approach to incorporate fairness into constrained spectral clustering for equitable representation of demographic groups. Fairness is incorporated into the pairwise constraint set by embedding a linear constraint that considers demographic group information into the spectral clustering objective function. A comprehensive set of experiments is conducted on real-world datasets, including Hepatitis, Census, and FriendshipNet, to evaluate the performance of the proposed approach. Clustering quality is assessed using the Rand Index, while fairness is measured using the Balance metric. The results demonstrate that the proposed fair constrained spectral clustering method effectively manages tradeoffs, achieving a higher Rand Index compared to spectral clustering and improved Balance compared to spectral clustering, constrained spectral clustering, and fair spectral clustering.