A significant drawback to existing RDF-based descriptors is that two structures identical apart from isotropic lattice expansion will give completely different RDFs. To test this, we have simulated 61 cubic (space group Pm-3m) perovskite structures with lattice constants ranging from 3 Å to 6 Å (Δa = 0.05 Å), chosen to coincide the range of cubic perovskite lattice constant found in the Project (3.05 Å-6.12 Å). Fig. shows the pairwise EMD between structures for each lattice constant, and reveals a continuous increase with lattice constant difference. It is intuitive that as a structure expands it becomes less similar to the starting point, but this is in stark contrast with the RDF (Fig. ) which shows discrete jumps in EMD across the same range. We attribute this behaviour to the significant degeneracy of interatomic distances at large separations in the RDF, and the different rate at which these change with isotropic expansion. As these distances move into different RDF bins during expansion, the minimum EMD changes discontinuously due to a change in EMD flow, as histogram 'mass' is preferentially moved to a different bin. A similar comparison using cosine distance (Fig. ) reveals that cosine distance using GRID only gives sensible dissimilarities for numerically close lattice parameters, while cosine distance on the RDF shows even more discontinuities than EMD.