Bcubed revisited: elements like me

Abstract

BCubed is a mathematically clean, elegant and intuitively well behaved external performance metric for clustering tasks. BCubed compares a predicted clustering to a known ground truth clustering through elementwise precision and recall scores. For each element, the predicted and ground truth clusters containing the element are compared, and the mean over all elements is taken. We argue that BCubed overestimates performance, for the intuitive reason that the clustering gets credit for putting an element into its own cluster. This is repaired, and we investigate the repaired version, called “Elements Like Me (ELM)”. We extensively evaluate ELM from both a theoretical and empirical perspective, and conclude that it retains all of its positive properties, and yields a minimum zero score when it should. Synthetic experiments show that ELM can produce different rankings of predicted clusterings when compared to BCubed, and that the ELM scores are distributed with lower mean and a larger variance than BCubed.