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. 2021 Nov 12;12:6576. doi: 10.1038/s41467-021-26752-4

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© The Author(s) 2021

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 6 — a Geographic position, shape, population, and distance between the Output Areas (OAs) E00137201 and E00137194, situated in Corby, England, a city with more than 50 thousand inhabitants (8th population decile). b, c Shapely values for the two flows between E00137201 (population of about 238 individuals) and E00137194 (population of about 223 individuals). Features are reported on the vertical axis, sorted from the most relevant on top to the least relevant on the bottom. The value of the feature is indicated in gray on the left of the feature name. The bars denote the contribution of each feature to the model’s prediction (the number inside or near the bar is the Shapely value). The sum of the Shapely values of all features is equal to the model’s prediction (f(x) denotes the score): feature with positive (negative) Shapely values push the flow probability to higher (lower) values with respect to the model’s average prediction E[f(x)]. Deep Gravity assigns different probabilities for the two flows and the Shapely values indicate that various geographical features are more relevant than the population in this case. The most relevant features for a specific origin-destination pair can differ from the most relevant features overall.