The first example is based on the Ruddlesden-Popper (R-P) series Srn+1TinO3n+1, which can be considered as a composite structure of variable-width perovskite units (width determined by n) separated by single rock-salt layers. Here we consider four structures (optimised using density functional theory, DFT) from the Materials Project (Fig. ): rock-salt SrO (n = 0, mp-2472), Sr2TiO4 (n = 1, mp-5532), Sr3Ti2O7 (n = 2, mp-3349) and perovskite SrTiO3 (n = ∞, mp-5229). The results of GRID dissimilarity calculated using EMD (Fig. ) show that the distance from SrO increases with n. This agrees with the chemical intuition; as n increases the ratio of rock-salt to perovskite layers reduces. Importantly, SrO (n = 0) and SrTiO3 (n = ∞) appear most dissimilar, as expected. In contrast, EMD calculated using the RDF (Fig. ) finds SrO and SrTiO3 to be the most similar pair, against chemical intuition. We have also tested the commonly used cosine distance (Fig. ) and find that although the same broad trend is reproduced using the GRID and RDF, the quantitative discrimination between the different R-P phases is much reduced.