Approximate entropy of network parameters

West, James and Lacasa Saiz de Arce, Lucas and Severini, Simone and Teschendorff, Andrew (2012). Approximate entropy of network parameters. "Physical Review e", v. 85 ; pp.. ISSN 1539-3755.


Title: Approximate entropy of network parameters
  • West, James
  • Lacasa Saiz de Arce, Lucas
  • Severini, Simone
  • Teschendorff, Andrew
Item Type: Article
Título de Revista/Publicación: Physical Review e
Date: 2012
Volume: 85
Faculty: E.T.S.I. Aeronáuticos (UPM)
Department: Matemática Aplicada y Estadística [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We first define a purely structural entropy obtained by computing the approximate entropy of the so-called slide sequence. This is a surrogate of the degree sequence and it is suggested by the frequency partition of a graph. We examine this quantity for standard scale-free and Erdös-Rényi networks. By using classical results of Pincus, we show that our entropy measure often converges with network size to a certain binary Shannon entropy. As a second step, with specific attention to networks generated by dynamical processes, we investigate approximate entropy of horizontal visibility graphs. Visibility graphs allow us to naturally associate with a network the notion of temporal correlations, therefore providing the measure a dynamical garment. We show that approximate entropy distinguishes visibility graphs generated by processes with different complexity. The result probes to a greater extent these networks for the study of dynamical systems. Applications to certain biological data arising in cancer genomics are finally considered in the light of both approaches.

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Item ID: 16707
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Deposited by: Memoria Investigacion
Deposited on: 05 Nov 2014 18:58
Last Modified: 13 Nov 2014 18:10
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