Fair Soft Clustering

Abstract

Scholars in the machine learning community have recently focused on analyzing the fairness of learning models, including clustering algorithms. In this work we study fair clustering in a probabilistic (soft) setting, where observations may belong to several clusters determined by probabilities. We introduce new probabilistic fairness metrics, which generalize and extend existing non-probabilistic fairness frameworks and propose an algorithm for obtaining a fair probabilistic cluster solution from a data representation known as a fairlet decomposition. Finally, we demonstrate our proposed fairness metrics and algorithm by constructing a fair Gaussian mixture model on three real-world datasets. We achieve this by identifying balanced micro-clusters which minimize the distances induced by the model, and on which traditional clustering can be performed while ensuring the fairness of the solution.