Towards Cohesion-Fairness Harmony: Contrastive Regularization in Individual Fair Graph Clustering
Siamak Ghodsi, Seyed Amjad Seyedi, Eirini Ntoutsi
TL;DR
The paper tackles fairness in unsupervised graph clustering by introducing iFairNMTF, a Fairness-aware Symmetric Nonnegative Matrix Tri-Factorization that incorporates a contrastive regularization term to enforce individual fairness while preserving cluster cohesion. It employs a joint objective $\min_{\bm{H},\bm{W}\ge 0} \lVert\bm{A}-\bm{H}\bm{W}\bm{H}^T\rVert^2_F + \lambda\,\text{Tr}(\bm{H}^T\bm{L}\bm{H})$, where $\bm{L}$ encodes contrastive relations between demographic groups, and updates are performed via multiplicative rules for $\bm{H}$ and $\bm{W}$. Key contributions include: (i) a flexible framework with an adjustable fairness parameter $\lambda$; (ii) a novel contrastive regularization promoting cross-group diversity within clusters; (iii) retention of interpretability through nonnegativity and an explicit cluster-interaction matrix $\bm{W}$; (iv) extensive experiments on real and synthetic data showing improved fairness (balance $B$) without sacrificing clustering quality (modularity $Q$). The approach provides practical, white-box control over fairness-cohesion trade-offs and offers interpretable insights into inter-cluster relationships, with potential impact on fair clustering in networked systems and beyond.
Abstract
Conventional fair graph clustering methods face two primary challenges: i) They prioritize balanced clusters at the expense of cluster cohesion by imposing rigid constraints, ii) Existing methods of both individual and group-level fairness in graph partitioning mostly rely on eigen decompositions and thus, generally lack interpretability. To address these issues, we propose iFairNMTF, an individual Fairness Nonnegative Matrix Tri-Factorization model with contrastive fairness regularization that achieves balanced and cohesive clusters. By introducing fairness regularization, our model allows for customizable accuracy-fairness trade-offs, thereby enhancing user autonomy without compromising the interpretability provided by nonnegative matrix tri-factorization. Experimental evaluations on real and synthetic datasets demonstrate the superior flexibility of iFairNMTF in achieving fairness and clustering performance.