The cumulative distributions and the mutual information decay function are plotted in Figure for both LoStOP and ElMD pairwise distances. The cumulative distributions and MI decay profile provide information on the underlying structure of the data. In Figure the LoStOP MI profile has a sharp drop followed by an extended decay. This implies that there are some dense (high similarity) materials but generally the data is fairly spread out. This is further emphasized by the fact that the mutual information cutoff occurs at ∼65% of the maximum observed distance. The cumulative distribution in this plot is also relatively flat at the outset indicating that most points have relatively few near neighbors. In contrast, the ElMD decay profile shown in Figure decays much quicker, indicating less distinction chemically. This is expected given that ∼70% of the control dataset are oxides. Several extreme outliers whose cumulative distribution deviate significantly are noted. Looking at these profiles ahead of the density analysis provides intuition for interpreting the computed densities. Plotting the densities along each axis reveals several interesting features of the dataset. Although this is not a clustering algorithm, materials with high similarity along one or more axes tend to to be near one another. The SiC polymorphs are identical in formula with minor structural variation.