# Difference between revisions of "Structure Similarity"

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The fingerprints from sites in a given structure are subsequently statistically processed to yield the minimum, maximum, mean, and standard deviation of each coordination percentage. The resultant ordered vector defines a structure fingerprint, '''v'''<sup>struct</sup>: | The fingerprints from sites in a given structure are subsequently statistically processed to yield the minimum, maximum, mean, and standard deviation of each coordination percentage. The resultant ordered vector defines a structure fingerprint, '''v'''<sup>struct</sup>: | ||

− | <math>\mathbf{v}^\mathrm{struct} = [min(w(\mathrm{CN}=1)), max(w(\mathrm{CN}=1)), mean(w(\mathrm{CN}=1)), | + | <math>\mathbf{v}^\mathrm{struct} = [</math> |

+ | |||

+ | <math>\min(w(\mathrm{CN}=1)), \max(w(\mathrm{CN}=1)), \mathrm{mean}(w(\mathrm{CN}=1)), \mathrm{std}(w(\mathrm{CN}=1)), \dots,</math> | ||

+ | |||

+ | <math>\min(w(\mathrm{CN}=12)), \max(w(\mathrm{CN}=12)), \mathrm{mean}(w(\mathrm{CN}=12)), \mathrm{std}(w(\mathrm{CN}=12))</math> | ||

+ | |||

+ | <math>]^\mathrm{T}</math> | ||

== Structure Distance == | == Structure Distance == |

## Revision as of 23:22, 7 March 2018

The similarity between two structures *i* and *j* is assessed on the basis of local coordination information from all sites in the two structures. ^{[1]} ^{[2]}

## Site Fingerprints

The similarity calculation begins with computing a crystal site fingerprint, **v**^{site}, for each site in the two structures. The fingerprint is a 12-dimensional vector in which an element at position *k* (e.g., 4) provides the percentage of how much the given site should be considered *k*-fold coordinated (i.e., *w*(CN=4)):

So, we are testing the coordination percentages up to 12-fold coordination.

## Structure Fingerprints

The fingerprints from sites in a given structure are subsequently statistically processed to yield the minimum, maximum, mean, and standard deviation of each coordination percentage. The resultant ordered vector defines a structure fingerprint, **v**^{struct}:

## Structure Distance

Finally, structure similarity is determined by the distance, *d*, between two structure fingerprints **v**_{i}^{struct} and **v**_{j}^{struct}:

A small distance value indicates high similarity between two structures, whereas a large distance (around 1) suggests that the structures are very dissimilar. Note that the structure fingerprint vectors are normalized before calculating the distance measure.

## References

- ↑ N. E. R. Zimmermann, A. Jain, in preparation (2018)
- ↑ N. E. R. Zimmermann, M. K. Horton, A. Jain, M. Haranczyk, Front. Mater., 4, 34, (2017)

## Authors

Nils Zimmermann, Donny Winston