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Improvement of Spatial Autocorrelation, Kernel Estimation, and Modeling Methods by Spatial Standardization on Distance

by Marc Souris 1,2,* and Florent Demoraes 3
1
UMR Unité des Virus Emergents (UVE: Aix-Marseille Univ—IRD 190—Inserm 1207—IHU Méditerranée Infection), 13005 Marseille, France
2
RS&GIS FoS, School of Engineering and Technology, Asian Institute of Technology, P.O. Box 4, Klong Luang, Pathumthani 12120, Thailand
3
Univ Rennes, CNRS, ESO—UMR 6590, F-35000 Rennes, France
*
Author to whom correspondence should be addressed.
ISPRS Int. J. Geo-Inf. 2019, 8(4), 199; https://doi.org/10.3390/ijgi8040199
Received: 5 March 2019 / Revised: 19 April 2019 / Accepted: 22 April 2019 / Published: 24 April 2019
In a point set in dimension superior to 1, the statistical distribution of the number of pairs of points as a function of distance between the points of the pair is not uniform. This distribution is not considered in a large number of classic methods based on spatially weighted means used in spatial analysis, such as spatial autocorrelation indices, kernel interpolation methods, or spatial modeling methods (autoregressive, or geographically weighted). It has a direct impact on the calculations and the results of indices and estimations, and by not taking into account this distribution of the distances, spatial analysis calculations can be biased. In this article, we introduce a “spatial standardization”, which corrects and adjusts the calculations with respect to the distribution of point pairs distances. As an example, we apply this correction to the calculation of spatial autocorrelation indices (Moran and Geary indices) and to trend surface calculation (by spatial kernel interpolation) on the results of the 2017 French presidential election. View Full-Text
Keywords: spatial analysis; spatial autocorrelation; spatial modeling; spatial kernel interpolation; standardization; SD-correction spatial analysis; spatial autocorrelation; spatial modeling; spatial kernel interpolation; standardization; SD-correction
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Souris, M.; Demoraes, F. Improvement of Spatial Autocorrelation, Kernel Estimation, and Modeling Methods by Spatial Standardization on Distance. ISPRS Int. J. Geo-Inf. 2019, 8, 199.

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