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Stability and statistical inferences in the space of topological spatial relationships

Corcoran, Padraig and Jones, Christopher 2018. Stability and statistical inferences in the space of topological spatial relationships. IEEE Access 6 , pp. 18907-18919. 10.1109/ACCESS.2018.2817493

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Abstract

Modelling topological properties of the spatial relationship between objects, known as the extit{topological relationship}, represents a fundamental research problem in many domains including Artificial Intelligence (AI) and Geographical Information Science (GIS). Real world data is generally finite and exhibits uncertainty. Therefore, when attempting to model topological relationships from such data it is useful to do so in a manner which is both extit{stable} and facilitates extit{statistical inferences}. Current models of the topological relationships do not exhibit either of these properties. We propose a novel model of topological relationships between objects in the Euclidean plane which encodes topological information regarding connected components and holes. Specifically, a representation of the persistent homology, known as a persistence scale space, is used. This representation forms a Banach space that is stable and, as a consequence of the fact that it obeys the strong law of large numbers and the central limit theorem, facilitates statistical inferences. The utility of this model is demonstrated through a number of experiments.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Computer Science & Informatics
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
ISSN: 2169-3536
Date of First Compliant Deposit: 29 March 2018
Date of Acceptance: 6 March 2018
Last Modified: 28 Apr 2019 12:18
URI: http://orca-mwe.cf.ac.uk/id/eprint/110300

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