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Fingerprint distances, which measure the similarity of atomic environments,are commonly calculated from atomic environment fingerprint vectors. In thiswork we present the simplex method which can perform the inverse operation,i.e. calculating fingerprint vectors from fingerprint distances. Thefingerprint vectors found in this way point to the corners of a simplex. For alarge data set of fingerprints, we can find a particular largest volumesimplex, whose dimension gives the effective dimension of the fingerprintvector space. We show that the corners of this simplex correspond to landmarkenvironments that can by used in a fully automatic way to analyse structures.In this way we can for instance detect atoms in grain boundaries or on edges ofcarbon flakes without any human input about the expected environment. Byprojecting fingerprints on the largest volume simplex we can also obtainfingerprint vectors that are considerably shorter than the original ones butwhose information content is not significantly reduced.

Maximum volume simplex method for automatic selection and classification of atomic environments and environment descriptor compression