Incorporating Fairness in Neighborhood Graphs for Fair Spectral Clustering

Abstract: Graph clustering plays a pivotal role in unsupervised learning methods like spectral clustering, yet traditional methods for graph clustering often perpetuate bias through unfair graph constructions that may underrepresent some groups. The current research introduces novel approaches for constructing fair k-nearest neighbor (kNN) and fair epsilon-neighborhood graphs that proactively enforce demographic parity during graph formation. By incorporating fairness constraints at the earliest stage of neighborhood selection steps, our approaches incorporate proportional representation of sensitive features into the local graph structure while maintaining geometric consistency.Our work addresses a critical gap in pre-processing for fair spectral clustering, demonstrating that topological fairness in graph construction is essential for achieving equitable clustering outcomes. Widely used graph construction methods like kNN and epsilon-neighborhood graphs propagate edge based disparate impact on sensitive groups, leading to biased clustering results. Providing representation of each sensitive group in the neighborhood of every node leads to fairer spectral clustering results because the topological features of the graph naturally reflect equitable group ratios. This research fills an essential shortcoming in fair unsupervised learning, by illustrating how topological fairness in graph construction inherently facilitates fairer spectral clustering results without the need for changes to the clustering algorithm itself. Thorough experiments on three synthetic datasets, seven real-world tabular datasets, and three real-world image datasets prove that our fair graph construction methods surpass the current baselines in graph clustering tasks.