Machine learning meets complex networks via coalescent embedding in the hyperbolic space

Alessandro Muscoloni, Josephine Maria Thomas, Sara Ciucci, Ginestra Bianconi and Carlo Vittorio Cannistraci ()
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Alessandro Muscoloni: Technische Universität Dresden
Josephine Maria Thomas: Technische Universität Dresden
Sara Ciucci: Technische Universität Dresden
Ginestra Bianconi: School of Mathematical Sciences, Queen Mary University of London
Carlo Vittorio Cannistraci: Technische Universität Dresden

Nature Communications, 2017, vol. 8, issue 1, 1-19

Abstract: Abstract Physicists recently observed that realistic complex networks emerge as discrete samples from a continuous hyperbolic geometry enclosed in a circle: the radius represents the node centrality and the angular displacement between two nodes resembles their topological proximity. The hyperbolic circle aims to become a universal space of representation and analysis of many real networks. Yet, inferring the angular coordinates to map a real network back to its latent geometry remains a challenging inverse problem. Here, we show that intelligent machines for unsupervised recognition and visualization of similarities in big data can also infer the network angular coordinates of the hyperbolic model according to a geometrical organization that we term “angular coalescence.” Based on this phenomenon, we propose a class of algorithms that offers fast and accurate “coalescent embedding” in the hyperbolic circle even for large networks. This computational solution to an inverse problem in physics of complex systems favors the application of network latent geometry techniques in disciplines dealing with big network data analysis including biology, medicine, and social science.

Date: 2017
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DOI: 10.1038/s41467-017-01825-5

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