Uncovering hidden nodes in complex networks in the presence of noise

Ri-Qi Su, Ying-Cheng Lai, Xiao Wang, Younghae Do

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Ascertaining the existence of hidden objects in a complex system, objects that cannot be observed from the external world, not only is curiosity-driven but also has significant practical applications. Generally, uncovering a hidden node in a complex network requires successful identification of its neighboring nodes,
but a challenge is to differentiate its effects from those of noise. We develop a completely data-driven, compressive-sensing based method to address this issue by utilizing complex weighted networks with continuous-time oscillatory or discrete-time evolutionary-game dynamics. For any node, compressive
sensing enables accurate reconstruction of the dynamical equations and coupling functions, provided that time series from this node and all its neighbors are available. For a neighboring node of the hidden node, this condition cannot be met, resulting in abnormally large prediction errors that, counterintuitively, can be used to infer the existence of the hidden node. Based on the principle of differential signal, we demonstrate that, when strong noise is present, insofar as at least two neighboring nodes of the hidden node are subject to weak background noise only, unequivocal identification of the hidden node can be achieved.
Original languageEnglish
Article number3944
JournalScientific Reports
Publication statusPublished - 3 Feb 2014

Bibliographical note

We thank Dr. W.-X. Wang for discussions. This work was supported by AFOSR under
Grant No. FA9550-10-1-0083 and by NSF under Grant. No. CDI-1026710, and by Basic
Science Research Program of the Ministry of Education, Science and Technology under
Grant No. NRF-2013R1A1A2010067, and by NSF under Grant No DMS-1100309 and by
Heart Association under Grant No 11BGIA7440101.


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