Difference between revisions of "Structure Similarity"
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| − | The similarity between two structures ''i'' and ''j'' is assessed on the basis of local coordination information from all sites in the two structures. | + | The similarity between two structures ''i'' and ''j'' is assessed on the basis of local coordination information from all sites in the two structures. <ref>N. E. R. Zimmermann, A. Jain, in preparation (2018)</ref> <ref>N. E. R. Zimmermann, M. K. Horton, A. Jain, M. Haranczyk, Front. Mater., 4, 34, (2017)</ref> |
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== Site Fingerprints == | == Site Fingerprints == | ||
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So, we are testing the coordination percentages up to 12-fold coordination. | So, we are testing the coordination percentages up to 12-fold coordination. | ||
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| + | == Structure Fingerprints == | ||
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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>: | ||
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| + | <math>\mathbf{v}^\mathrm{struct} = [min(w(\mathrm{CN}=1)), max(w(\mathrm{CN}=1)), mean(w(\mathrm{CN}=1)), std(w(\mathrm{CN}=1)), min(w(\mathrm{CN}=2)), \dots, min(w(\mathrm{CN}=12)), max(w(\mathrm{CN}=12)), mean(w(\mathrm{CN}=12)), std(w(\mathrm{CN}=12))]^\mathrm{T}</math> | ||
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| + | == Structure Distance == | ||
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| + | Finally, structure similarity is determined by the distance, ''d'', between two structure fingerprints '''v'''<sub>i</sub><sup>struct</sup> and '''v'''<sub>j</sub><sup>struct</sup>: | ||
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| + | <math>d = || \mathbf{v}_{i}^\mathrm{struct} - \mathbf{v}_{j}^\mathrm{struct} ||</math> | ||
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| + | 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 == | == References == | ||
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== Authors == | == Authors == | ||
| − | + | Nils Zimmermann, Donny Winston | |
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Revision as of 23:10, 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, vsite, 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)):
![\mathbf{v}^\mathrm{site} = [w(\mathrm{CN}=1), w(\mathrm{CN}=2), w(\mathrm{CN}=3), \dots, w(\mathrm{CN}=12)]^\mathrm{T}](/images/math/4/7/f/47f56a5b516bb422b069977770b94e37.png)
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, vstruct:
![\mathbf{v}^\mathrm{struct} = [min(w(\mathrm{CN}=1)), max(w(\mathrm{CN}=1)), mean(w(\mathrm{CN}=1)), std(w(\mathrm{CN}=1)), min(w(\mathrm{CN}=2)), \dots, min(w(\mathrm{CN}=12)), max(w(\mathrm{CN}=12)), mean(w(\mathrm{CN}=12)), std(w(\mathrm{CN}=12))]^\mathrm{T}](/images/math/c/b/b/cbbb63ff723f205076a14dfbc33272d4.png)
Structure Distance
Finally, structure similarity is determined by the distance, d, between two structure fingerprints vistruct and vjstruct:
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
