Enhancing Fairness in Gaussian Mixture Clustering through Impact Factor

Clustering is a common method used in machine learning to group sample points in a dataset. Gaussian Mixture Clustering (GMC) is a clustering method based on maximum likelihood estimation and expectation maximisation (EM) algorithms. Traditional GMC does not consider the fairness between different sensitive groups, leading to biased clustering results. In this paper, we propose a novel Fair Gaussian Mixture Clustering (FGMC) to solve the fairness problem in clustering tasks. We incorporate a fairness optimiser, the impact factor, into the GMC to ensure that the fairness of the clustering is gradually optimised over the iterations. Using FGMC ensures that the clustering results are not overly biased towards a particular group defined by sensitive attributes such as age or race. We evaluated FGMC on a real-world dataset and found that it significantly improved clustering fairness. FGMC is a promising direction for clustering that requires ethical considerations.