Accelerating Spectral Clustering under Fairness Constraints

2025-06-09

AI Summary

This work addresses spectral clustering under group fairness constraints—requiring each cluster to preserve the global demographic proportion across protected subgroups. We propose the first Difference-of-Convex (DC) optimization framework for this problem. Our method introduces a variable-augmentation strategy to circumvent the computationally expensive eigen-decomposition of the Laplacian matrix inherent in conventional approaches. We further design an Alternating Direction Method of Multipliers (ADMM)-based algorithm, incorporating efficient specialized solvers for its subproblems. Experiments on both synthetic and real-world datasets demonstrate that our approach significantly improves computational efficiency: it achieves several-fold speedup over state-of-the-art fair spectral clustering methods, especially at scale. The framework thus provides a scalable, high-accuracy paradigm for practical deployment of fair clustering.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Clustering
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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.

Problem

• Ensures fair representation in spectral clustering groups
• Improves computational efficiency of fair clustering algorithms
• Reduces reliance on expensive eigendecomposition in clustering

Innovation

• Fair SC using difference of convex functions
• Novel variable augmentation strategy
• Efficient ADMM algorithm for DC problems