An entropy-driven matrix completion (E-MC) approach to complex network mapping

Ali Koochakzadeh; Piya Pal

doi:10.1117/12.2223430

4 May 2016 An entropy-driven matrix completion (E-MC) approach to complex network mapping

Ali Koochakzadeh, Piya Pal

Proceedings Volume 9857, Compressive Sensing V: From Diverse Modalities to Big Data Analytics; 985703 (2016) https://doi.org/10.1117/12.2223430
Event: SPIE Commercial + Scientific Sensing and Imaging, 2016, Baltimore, MD, United States

Abstract

Mapping the topology of a complex network in a resource-efficient manner is a challenging problem with applications in internet mapping, social network inference, and so forth. We propose a new entropy driven algorithm leveraging ideas from matrix completion, to map the network using monitors (or sensors) which, when placed on judiciously selected nodes, are capable of discovering their immediate neighbors. The main challenge is to maximize the portion of discovered network using only a limited number of available monitors. To this end, (i) a new measure of entropy or uncertainty is associated with each node, in terms of the currently discovered edges incident on that node, and (ii) a greedy algorithm is developed to select a candidate node for monitor placement based on its entropy. Utilizing the fact that many complex networks of interest (such as social networks), have a low-rank adjacency matrix, a matrix completion algorithm, namely 1-bit matrix completion, is combined with the greedy algorithm to further boost its performance. The low rank property of the network adjacency matrix can be used to extrapolate a portion of missing edges, and consequently update the node entropies, so as to efficiently guide the network discovery algorithm towards placing monitors on the nodes that can turn out to be more informative. Simulations performed on a variety of real world networks such as social networks and peer networks demonstrate the superior performance of the matrix-completion guided approach in discovering the network topology.

Citation Download Citation

Ali Koochakzadeh and Piya Pal "An entropy-driven matrix completion (E-MC) approach to complex network mapping", Proc. SPIE 9857, Compressive Sensing V: From Diverse Modalities to Big Data Analytics, 985703 (4 May 2016); https://doi.org/10.1117/12.2223430

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KEYWORDS

Social networks

Algorithm development

Internet

Signal processing

Tomography

Convex optimization

Image information entropy

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