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Journal of Geographical Systems
Published in: Journal of Geographical Systems 4/2015

01-10-2015 | Original Article

Optimizing distance-based methods for large data sets

Authors: Tobias Scholl, Thomas Brenner

Published in: Journal of Geographical Systems | Issue 4/2015

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Abstract

Distance-based methods for measuring spatial concentration of industries have received an increasing popularity in the spatial econometrics community. However, a limiting factor for using these methods is their computational complexity since both their memory requirements and running times are in \({\mathcal {O}}(n^2)\). In this paper, we present an algorithm with constant memory requirements and shorter running time, enabling distance-based methods to deal with large data sets. We discuss three recent distance-based methods in spatial econometrics: the D&O-Index by Duranton and Overman (Rev Econ Stud 72(4):1077–1106, 2005), the M-function by Marcon and Puech (J Econ Geogr 10(5):745–762, 2010) and the Cluster-Index by Scholl and Brenner (Reg Stud (ahead-of-print):1–15, 2014). Finally, we present an alternative calculation for the latter index that allows the use of data sets with millions of firms.
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Footnotes
1
Note, that Eq. (2) is modified for the observation of an unmarked point pattern. See Marcon and Puech (2010, p. 749) for the original formula of the M-function.
 
2
Note, that the latest version of dbmss already includes computational improvements. See Sect. 4 for more information.
 
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Metadata
Title
Optimizing distance-based methods for large data sets
Authors
Tobias Scholl
Thomas Brenner
Publication date
01-10-2015
Publisher
Springer Berlin Heidelberg
Published in
Journal of Geographical Systems / Issue 4/2015
Print ISSN: 1435-5930
Electronic ISSN: 1435-5949
DOI
https://doi.org/10.1007/s10109-015-0219-1

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