FairAD: Computationally Efficient Fair Graph Clustering via Algebraic Distance

TL;DR

FairAD introduces a fast and efficient method for fair graph clustering that maintains demographic fairness while significantly reducing computational time, suitable for large-scale graphs.

Contribution

It proposes a novel affinity matrix construction and graph coarsening approach to incorporate fairness constraints efficiently in graph clustering.

Findings

Achieves fair clustering with demographic proportionality.

Up to 40 times faster than existing methods.

Effective on multiple datasets and models.

Abstract

Due to the growing concern about unsavory behaviors of machine learning models toward certain demographic groups, the notion of 'fairness' has recently drawn much attention from the community, thereby motivating the study of fairness in graph clustering. Fair graph clustering aims to partition the set of nodes in a graph into $k$ disjoint clusters such that the proportion of each protected group within each cluster is consistent with the proportion of that group in the entire dataset. It is, however, computationally challenging to incorporate fairness constraints into existing graph clustering algorithms, particularly for large graphs. To address this problem, we propose FairAD, a computationally efficient fair graph clustering method. It first constructs a new affinity matrix based on the notion of algebraic distance such that fairness constraints are imposed. A graph coarsening process is then performed on this affinity matrix to find representative nodes that correspond to $k$ clusters. Finally, a constrained minimization problem is solved to obtain the solution of fair clustering. Experiment results on the modified stochastic block model and six public datasets show that FairAD can achieve fair clustering while being up to 40 times faster compared to state-of-the-art fair graph clustering algorithms.