The other validation method is a LOCO-CV approach using cumulative density function (CDF) distance (i.e. Earth Mover's or Wasserstein distance) as a metric to determine the sorted similarity of a predicted cluster property vs. a true cluster property using scipy.stats.wasserstein distance() as follows : where avg_true and avg_pred represent the 1D array of DFT-calculated average bulk moduli for each cluster and the 1D array of predicted average bulk moduli for each cluster, respectively, given by Eq. ( ). The use of a cumulative sum causes the positions of high cluster bulk modulus averages to be further spaced apart and therefore is more costly to "move earth" between the two distributions. In other words, inaccuracies associated with high-performing clusters are weighted more heavily than inaccuracies for low-performing clusters. This weighted error is then scaled by dividing by a "dummy" error, where v_weights is replaced by the average bulk modulus of the training data for each of the training splits (as opposed to the predictions on the validation data) during computation of the Wasserstein distance.