Paper Info
Title
Stability and Statistical Inferences in the Space of Topological Spatial Relationships.
Abstract
Modeling topological properties of the spatial relationship between objects, known as the topological relationship, represent a fundamental research problem in many domains including artificial intelligence and geographical information science. Real-world data are generally finite and exhibit uncertainty. Therefore, when attempting to model topological relationships from such data, it is useful to do so in a manner which is both stable and facilitates 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.
Year
DOI
Venue
2018
10.1109/ACCESS.2018.2817493
IEEE ACCESS
Keywords
Field
DocType
Spatial relationships,topology,stable,statistical inference
Topology,Data modeling,Central limit theorem,Computer science,Law of large numbers,Banach space,Persistent homology,Connected component,Statistical inference,Euclidean geometry
Journal
Volume
ISSN
Citations 
6
2169-3536
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Padraig Corcoran119123.08
Christopher B. Jones2106795.29