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Representing higher-order dependencies in networks.

Jian Xu1, Thanuka L Wickramarathne2, Nitesh V Chawla3

  • 1Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN 46556, USA.; Interdisciplinary Center for Network Science and Applications, University of Notre Dame, Notre Dame, IN 46556, USA.Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA.Environmental Change Initiative, University of Notre Dame, Notre Dame, IN 46556, USA.

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|July 8, 2016
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Summary
This summary is machine-generated.

Conventional network analysis struggles with complex sequential data. Higher-order networks (HON) capture multi-step dependencies, improving accuracy for tasks like shipping traffic analysis.

Keywords:
MarkovianNetwork scienceclusteringcommunity detectiondata miningnetwork structurerandom walkranking

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Area of Science:

  • Network Science
  • Data Analysis
  • Complex Systems

Background:

  • Network analysis accuracy depends on data representation.
  • Traditional methods assume first-order Markov property, limiting analysis of sequential data like web traffic.
  • Complex systems often exhibit dependencies beyond the first order.

Purpose of the Study:

  • To address limitations of first-order network representations for sequential data.
  • To propose a novel network representation capturing higher-order dependencies.
  • To evaluate the accuracy, scalability, and applicability of the proposed method.

Main Methods:

  • Development of the higher-order network (HON) representation.
  • Embedding variable orders of dependencies into network structures.
  • Empirical evaluation on sequential datasets, including global shipping and web clickstream data.

Main Results:

  • Demonstrated that complex systems can have dependencies up to fifth-order.
  • HON accurately captures these higher-order dependencies.
  • HON shows accuracy, scalability, and compatibility with existing network analysis tools.

Conclusions:

  • Higher-order network representation overcomes limitations of first-order assumptions.
  • HON provides more accurate results for network analysis tasks like random walking, clustering, and ranking.
  • HON is a versatile tool for analyzing complex sequential data across various domains.