1. Maximum volume simplex method for automatic selection and classification of atomic environments and environment descriptor compression
- Author
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Stefan Goedecker, Behnam Parsaeifard, Deb Sankar De, and Daniele Tomerini
- Subjects
Similarity (geometry) ,Computer science ,Data_MISCELLANEOUS ,FOS: Physical sciences ,General Physics and Astronomy ,010402 general chemistry ,01 natural sciences ,Simplex algorithm ,Dimension (vector space) ,0103 physical sciences ,Computer Science::Multimedia ,Point (geometry) ,Physical and Theoretical Chemistry ,Computer Science::Databases ,Computer Science::Cryptography and Security ,Condensed Matter - Materials Science ,Simplex ,010304 chemical physics ,business.industry ,Fingerprint (computing) ,Materials Science (cond-mat.mtrl-sci) ,Pattern recognition ,Computational Physics (physics.comp-ph) ,Effective dimension ,0104 chemical sciences ,Computer Science::Computer Vision and Pattern Recognition ,Artificial intelligence ,business ,Physics - Computational Physics ,Vector space - Abstract
Fingerprint distances, which measure the similarity of atomic environments, are commonly calculated from atomic environment fingerprint vectors. In this work we present the simplex method which can perform the inverse operation, i.e. calculating fingerprint vectors from fingerprint distances. The fingerprint vectors found in this way point to the corners of a simplex. For a large data set of fingerprints, we can find a particular largest volume simplex, whose dimension gives the effective dimension of the fingerprint vector space. We show that the corners of this simplex correspond to landmark environments 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 of carbon flakes without any human input about the expected environment. By projecting fingerprints on the largest volume simplex we can also obtain fingerprint vectors that are considerably shorter than the original ones but whose information content is not significantly reduced., Comment: 10 pages, 7 figures
- Published
- 2020
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