Data-based reconstruction of complex geospatial networks, nodal positioning and detection of hidden nodes

Riqi just sent me the following:

Dear Dr. Igor Carron,

I hope this email finds you well. 

This is Riqi Su, a loyal audience of your blog from Arizona State University. I am very glad to share my new paper on hidden node detection with compressive sensing which publishes in Royal Society Open Science today. Its title is 'Data-based reconstruction of complex geospatial networks, nodal positioning and detection of hidden nodes'.

Actually, this paper is a succession to our previous works on compressive sensing and hidden node detection, which you reported on your blog in May, 2012:

http://nuit-blanche.blogspot.com/2012/05/reverse-engineering-biochemical.html

and another blog in Apr, 2011

http://nuit-blanche.blogspot.com/2011/04/cs-replica-method-for-sparse.html

We sincerely appreciate your interests on our research group lead by Prof. Ying-Cheng Lai from the School of Electrical, Computer and Energy Engineering, Arizona State University.

The abstract reads:

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 neighboring 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.

And it can be highlighted by its Fig. 2:

It shows that, solely using time series collected from spatially distributed objects, we can accurately reconstruct their connection pattern, nodal dynamics and spatial locations. We can then locate the hidden node by identifying all its neighboring nodes with abnormal reconstructed results from compressive sensing (Fig. 7):

Best,

Riqi Su,  Ph.D
Postdoctoral Research Associate
School of Biological and Health Systems Engineering, 

Arizona State University, Tempe, AZ 85287

Thanks Riqi !

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