We have found that with no supervision, the use of this metric gives a distinct partitioning of binary compounds into clear trends and families of chemical property, with future applications for nearest neighbor search queries in chemical database retrieval systems and supervised ML techniques. The EMD is a reliable numeric measure of chemical similarity that can be incorporated into automated workflows for a range of ML techniques. The resultant distances have greater alignment with chemical understanding than the Euclidean distance, which is demonstrated on the binary compositions of the inorganic crystal structure database. This simple metric shows clear strength at distinguishing compounds and is efficient to compute in practice. We compute the EMD between two compositions from the ratio of each of the elements and the absolute distance between the elements on the modified Pettifor scale. We present the earth mover’s distance (EMD) for inorganic compositions, a well-defined metric which enables the measure of chemical similarity in an explainable fashion. These vectors are a convenient mathematical data structure for measuring similarity, but unfortunately, the standard metric (the Euclidean distance) gives little to no variance in the resultant distances between chemically dissimilar compositions. For inorganic solids, the chemical composition is a fundamental descriptor, which can be represented by assigning the ratio of each element in the material to a vector. It is a core problem in any field to reliably tell how close two objects are to being the same, and once this relation has been established, we can use this information to precisely quantify potential relationships, both analytically and with machine learning (ML).
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