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Volume entropy and information flow in a brain graph

Hyekyoung Lee,Hyejin Kang,Eunkyung Kim,Y. Huh,Youngjo Lee,Seonhee Lim,Dong Soo Lee

Published 2018 in arXiv: Neurons and Cognition

ABSTRACT

Entropy is a classical measure to quantify the amount of information or complexity of a system. Various entropy-based measures such as functional and spectral entropies have been proposed in brain network analysis. However, they are less widely used than traditional graph theoretic measures such as global and local efficiencies because either they are not well-defined on a graph or difficult to interpret its biological meaning. In this paper, we propose a new entropy-based graph invariant, called volume entropy. It measures the exponential growth rate of the number of paths in a graph, which is a relevant measure if information flows through the graph forever. We model the information propagation on a graph by the generalized Markov system associated to the weighted edge-transition matrix. We estimate the volume entropy using the stationary equation of the generalized Markov system. A prominent advantage of using the stationary equation is that it assigns certain distribution of weights on the edges of the brain graph, which we call the stationary distribution. The stationary distribution shows the information capacity of edges and the direction of information flow on a brain graph. The simulation results show that the volume entropy distinguishes the underlying graph topology and geometry better than the existing graph measures. In brain imaging data application, the volume entropy of brain graphs was significantly related to healthy normal aging from 20s to 60s. In addition, the stationary distribution of information propagation gives a new insight into the information flow of functional brain graph.

PUBLICATION RECORD

  • Publication year

    2018

  • Venue

    arXiv: Neurons and Cognition

  • Publication date

    2018-01-28

  • Fields of study

    Biology, Computer Science

  • Identifiers
    arXiv 1801.09257
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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