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

Behnam Parsaeifard1, Daniele Tomerini1, Deb Sankar De1

  • 1Department of Physics, Universitaet Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland.

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Summary
This summary is machine-generated.

The simplex method calculates atomic fingerprint vectors from distances, revealing landmark atomic environments. This approach automatically analyzes structures and reduces data dimensionality without losing information.

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Area of Science:

  • Materials Science
  • Computational Chemistry
  • Data Analysis

Background:

  • Atomic environment fingerprint vectors are crucial for calculating fingerprint distances, which quantify atomic environment similarity.
  • Current methods primarily focus on calculating distances from vectors, lacking an efficient inverse operation.

Purpose of the Study:

  • To introduce the simplex method for calculating fingerprint vectors from fingerprint distances.
  • To demonstrate the utility of the simplex method in identifying landmark atomic environments and reducing data dimensionality.

Main Methods:

  • Developed the simplex method to perform the inverse operation of calculating fingerprint vectors from fingerprint distances.
  • Applied the method to large datasets to identify the largest simplex and its dimension, representing the effective dimension of the fingerprint vector space.
  • Utilized fingerprint projection onto the largest simplex for dimensionality reduction.

Main Results:

  • The simplex method successfully calculates fingerprint vectors from distances.
  • The corners of the largest simplex correspond to landmark atomic environments, enabling automatic structural analysis.
  • Demonstrated the ability to detect atoms in grain boundaries or on edges of carbon flakes without prior environmental knowledge.
  • Achieved significant reduction in fingerprint vector length through projection, preserving essential information content.

Conclusions:

  • The simplex method provides an effective inverse operation for atomic fingerprint analysis.
  • Landmark environments identified via the simplex method facilitate automated structural analysis and feature detection.
  • Dimensionality reduction via simplex projection offers a computationally efficient way to represent atomic environments.