In place of the median expression value in the numerator of the original ZE(j), we multiplied the sample's median gene expression value with the expression values for each individual gene within the cluster, and computed the mean of the resulting vector. Although this strategy will produce a higher Z2E(j) in the case of a cluster with strongly driven outliers, it will also produce a lower Z2E(j) in the presence of weakly driven outliers, even when the cluster is otherwise strongly driven. Thus, a larger priority was given to penalizing strongly driven clusters with weakly driven outliers than the opposite. Overall, this produced smaller values of Z2E(j) and gave a slightly greater dispersion of clusters with outliers when compared to taking the median gene expression value (not shown). Our software implementation provides a choice of either calculation for the numerator.
