Spectral Normalized-Cut Graph Partitioning with Fairness Constraints

TL;DR

This paper introduces a spectral clustering algorithm that incorporates fairness constraints to ensure demographic representation in graph partitioning, demonstrating improved results on benchmark datasets.

Contribution

The paper proposes a novel two-phase spectral algorithm, FNM, that integrates fairness into normalized-cut graph partitioning with a new fairness-aware embedding and rounding scheme.

Findings

FNM outperforms baseline methods on benchmark datasets.

The fairness constraints effectively balance demographic representation and partition quality.

Experimental results validate the method's superiority in fairness and clustering performance.

Abstract

Normalized-cut graph partitioning aims to divide the set of nodes in a graph into $k$ disjoint clusters to minimize the fraction of the total edges between any cluster and all other clusters. In this paper, we consider a fair variant of the partitioning problem wherein nodes are characterized by a categorical sensitive attribute (e.g., gender or race) indicating membership to different demographic groups. Our goal is to ensure that each group is approximately proportionally represented in each cluster while minimizing the normalized cut value. To resolve this problem, we propose a two-phase spectral algorithm called FNM. In the first phase, we add an augmented Lagrangian term based on our fairness criteria to the objective function for obtaining a fairer spectral node embedding. Then, in the second phase, we design a rounding scheme to produce $k$ clusters from the fair embedding that effectively trades off fairness and partition quality. Through comprehensive experiments on nine benchmark datasets, we demonstrate the superior performance of FNM compared with three baseline methods.