On the Use of Spearman's Rho to Measure the Stability of Feature Rankings

Producing stable feature rankings is critical in many areas, such as in bioinformatics where the robustness of a list of ranked genes is crucial to interpretation by a domain expert. In this paper, we study Spearman's rho as a measure of stability to training data perturbations not just as a heuristic, but here proving that it is the natural measure of stability when using mean rank aggregation. We provide insights on the properties of this stability measure, allowing a useful interpretation of stability values - e.g. how close a stability value is to that of a purely random feature ranking process, and concepts such as the expected value of a stability estimator.