Accelerating Spectral Clustering under Fairness Constraints

TL;DR

This paper introduces a new efficient method for fair spectral clustering that ensures demographic groups are proportionally represented, significantly reducing computation time compared to previous approaches.

Contribution

We propose a novel fair spectral clustering algorithm using a difference of convex functions framework with an efficient variable augmentation and optimization strategy.

Findings

Significant speedups in computation time over prior methods.

Effective fair clustering demonstrated on synthetic and real-world data.

Scalability improvements for large datasets.

Abstract

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.