Accelerating Spectral Clustering under Fairness Constraints
This work addresses the need for fair clustering algorithms in real-world applications, representing an incremental improvement in computational efficiency for a specific domain.
The paper tackles the problem of spectral clustering under group fairness constraints by proposing a new efficient method that reduces computational cost, achieving significant speedups in computation time compared to prior work, especially for larger problem sizes.
Fairness of decision-making algorithms is an increasingly important issue. In this paper, we focus on spectral clustering with group fairness constraints, where every demographic group is represented in each cluster proportionally as in the general population. We present a new efficient method for fair spectral clustering (Fair SC) by casting the Fair SC problem within the difference of convex functions (DC) framework. To this end, we introduce a novel variable augmentation strategy and employ an alternating direction method of multipliers type of algorithm adapted to DC problems. We show that each associated subproblem can be solved efficiently, resulting in higher computational efficiency compared to prior work, which required a computationally expensive eigendecomposition. Numerical experiments demonstrate the effectiveness of our approach on both synthetic and real-world benchmarks, showing significant speedups in computation time over prior art, especially as the problem size grows. This work thus represents a considerable step forward towards the adoption of fair clustering in real-world applications.