  The Fairness, Accountability, and Transparency in Machine Learning (FAT-ML)
literature proposes a varied set of group fairness metrics to measure
discrimination against socio-demographic groups that are characterized by a
protected feature, such as gender or race.Such a system can be deemed as either
fair or unfair depending on the choice of the metric. Several metrics have been
proposed, some of them incompatible with each other.We do so empirically, by
observing that several of these metrics cluster together in two or three main
clusters for the same groups and machine learning methods. In addition, we
propose a robust way to visualize multidimensional fairness in two dimensions
through a Principal Component Analysis (PCA) of the group fairness metrics.
Experimental results on multiple datasets show that the PCA decomposition
explains the variance between the metrics with one to three components.
