title: Data-based reconstruction of complex geospatial networks, nodal positioning and detection of hidden nodes.
abstract: Given a complex geospatial network with nodes distributed in a two-dimensional region of physical space, can the locations of the nodes be determined and their connection patterns be uncovered based solely on data? We consider the realistic situation where time series/signals can be collected from a single location. A key challenge is that the signals collected are necessarily time delayed, due to the varying physical distances from the nodes to the data collection centre. To meet this challenge, we develop a compressive-sensing-based approach enabling reconstruction of the full topology of the underlying geospatial network and more importantly, accurate estimate of the time delays. A standard triangularization algorithm can then be employed to find the physical locations of the nodes in the network. We further demonstrate successful detection of a hidden node (or a hidden source or threat), from which no signal can be obtained, through accurate detection of all its neighbouring nodes. As a geospatial network has the feature that a node tends to connect with geophysically nearby nodes, the localized region that contains the hidden node can be identified.
authors.affiliation: School of Electrical, Computer, and Energy Engineering , Arizona State University , Tempe, AZ 85287, USA.
authors.forename: Ri-Qi
authors.initials: RQ
authors.lastname: Su
authors.affiliation: Department of Systems Science, School of Management and Center for Complexity Research , Beijing Normal University , Beijing 100875, People's Republic of China.
authors.forename: Wen-Xu
authors.initials: WX
authors.lastname: Wang
authors.affiliation: School of Biological and Health Systems Engineering , Arizona State University , Tempe, AZ 85287, USA.
authors.forename: Xiao
authors.initials: X
authors.lastname: Wang
authors.affiliation: School of Electrical, Computer, and Energy Engineering , Arizona State University , Tempe, AZ 85287, USA.
authors.forename: Ying-Cheng
authors.initials: YC
authors.lastname: Lai
keywords: compressive sensing; geospatial network; network reconstruction; time-series analysis