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

TL;DR

This paper introduces a maximum volume simplex method that automatically identifies key atomic environments and compresses environment descriptors, enabling unsupervised structure analysis and reduced fingerprint vector size.

Contribution

The novel maximum volume simplex approach allows automatic environment classification and fingerprint compression without prior knowledge or human input.

Findings

Identifies landmark atomic environments automatically.

Enables significant fingerprint vector compression.

Detects specific atomic features like grain boundaries.

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.