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A framework for assisted proximity analysis in feature data

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Abstract

This framework for assisted proximity analysis in feature data consists of a hierarchy of proximity classes that use spatial neighborhoods as fundamental building blocks. The instances are spatial relations between isolated objects, or objects in a cluster, sharing the relational properties of reflexivity/irreflexivity and symmetry/asymmetry. The framework proposes ways of generating spatial neighborhoods and includes a discussion of how to deal with the vagueness inherent in nearness relations. It is applied to a realistic use case of epizootic disease outbreak. The framework updates the current state of knowledge in the field by considering: (1) spatial objects in a cluster, (2) spatially coextensive regions, and (3) regions in a partition chain. It relates ways of generating spatial neighborhoods to the proximity classes and introduces a number of yes–no questions to be implemented as a sequence of functions in a GIS system. The objective of the latter is to assist non-expert users, such as decision-makers, in carrying out proximity analyses. This is the first time that such a comprehensive framework has been proposed.

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Notes

  1. http://desktop.arcgis.com/en/arcmap/10.3/analyze/commonly-used-tools/proximity-analysis.htm.

  2. The \(\delta\)-notation for proximity is borrowed from Efremovič (1951). The superscript 1 is a sequence number, the subscript s indicates that the relations of this proximity class are symmetric. Superscript and subscript are aligned with those in Brennan and Martin (2012).

  3. Brennan and Martin (2012) omit the conjunct \((IA(x)\ \cap \ y\ = \emptyset )\) in \(Near^{3}_{a}\). The subscript a indicates that the relations of this proximity class are asymmetric.

  4. Worboys (2001) uses a similar example to motivate the notion of weak symmetry which is interpreted in a four-valued logic (Belnap 1977): Keele, a village in the vicinity of the city of Stoke-on-Trent, can be thought of as being near Stoke-on-Trent, but the converse is less true.

  5. Conversely, the proximity notions \(Near^{2}_{a}\) and \(Near^{5}_{a}\) in Brennan and Martin (2012) are not considered in this article. \(Near^{2}_{a}\) imposes a metric restriction on the relative extents of two intersecting impact areas, \(Near^{5}_{a}\) defines the special case where one impact area is subsumed by the other.

  6. https://en.oxforddictionaries.com/.

  7. It is worth noting that \(\biguplus _{i=1}^{n}\) is the inline notation of the symbol used in Eq. 6.

  8. A set of points is said to be convex if it contains the straight line segments connecting each pair of its points.

  9. In an asymmetric case, x cannot be in the same cluster as \(y_{i}\) since \(\delta ^{5}\) is by definition symmetric inside a cluster.

  10. In ArcGIS (https://www.arcgis.com/), impact areas can be generated in this way by computing so-called service areas.

  11. https://www.english-corpora.org/coca/.

  12. https://www.english-corpora.org/wiki/.

  13. The design of the experiment was such that not near might have been a surrogate masking antonymical predicates such as far. Assuming that near and far are no strict antonyms, then the structure underlying the data could also be described in the two-valued logic used in the framework presented here: \(near \wedge far\) (empty set), \(near \wedge \lnot far\) (nearness neighborhood), \(\lnot near \wedge \lnot far\) (broad boundary), and \(\lnot near \wedge far\) (area beyond the boundary).

  14. https://www.ge.ch/document/rapport-gestion-2006-du-conseil-etat-republique-canton-geneve.

  15. http://desktop.arcgis.com/en/arcmap/10.3/tools/coverage-toolbox/buffer.htm.

  16. http://desktop.arcgis.com/en/arcmap/10.3/map/working-with-layers/using-select-by-location.htm.

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Acknowledgements

A special thanks to Professor Harold Boley, Ph.D., of the University of New Brunswick, NB, Canada, and Marc Novel of the Swiss Federal Research Institute WSL, Birmensdorf, and the University of Zurich for the extensive discussions of important aspects of this article. The help of Silvia Dingwall, Ph.D. in Applied Linguistics, with language editing is gratefully acknowledged. This research was funded by the Swiss Federal Office for the Environment (FOEN).

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    Rolf Grütter

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Grütter, R. A framework for assisted proximity analysis in feature data. J Geogr Syst 21, 367–394 (2019). https://doi.org/10.1007/s10109-019-00304-3

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