A Unified Framework for Fair Spectral Clustering With Effective Graph Learning

TL;DR

This paper introduces a unified, end-to-end framework for fair spectral clustering that learns the underlying graph from noisy data and integrates all steps into a single optimization, improving fairness and clustering quality.

Contribution

It proposes a novel graph construction method with a node-adaptive filter and unifies all stages of fair spectral clustering into an end-to-end model.

Findings

Outperforms state-of-the-art fair clustering methods on various datasets.

Effectively constructs graphs from noisy data, enhancing clustering fairness.

Demonstrates robustness and improved accuracy in experiments.

Abstract

We consider the problem of spectral clustering under group fairness constraints, where samples from each sensitive group are approximately proportionally represented in each cluster. Traditional fair spectral clustering (FSC) methods consist of two consecutive stages, i.e., performing fair spectral embedding on a given graph and conducting $k$means to obtain discrete cluster labels. However, in practice, the graph is usually unknown, and we need to construct the underlying graph from potentially noisy data, the quality of which inevitably affects subsequent fair clustering performance. Furthermore, performing FSC through separate steps breaks the connections among these steps, leading to suboptimal results. To this end, we first theoretically analyze the effect of the constructed graph on FSC. Motivated by the analysis, we propose a novel graph construction method with a node-adaptive graph filter to learn graphs from noisy data. Then, all independent stages of conventional FSC are integrated into a single objective function, forming an end-to-end framework that inputs raw data and outputs discrete cluster labels. An algorithm is developed to jointly and alternately update the variables in each stage. Finally, we conduct extensive experiments on synthetic, benchmark, and real data, which show that our model is superior to state-of-the-art fair clustering methods.