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Maps of sparse Markov chains efficiently reveal community structure in network flows with memory
Umeå University, Faculty of Science and Technology, Department of Physics. (IceLab)
Umeå University, Faculty of Science and Technology, Department of Physics. (IceLab)
Umeå University, Faculty of Science and Technology, Department of Physics. (IceLab)
Umeå University, Faculty of Science and Technology, Department of Physics. (IceLab)
(English)Manuscript (preprint) (Other academic)
Abstract [en]

To better understand the flows of ideas or information through social and biological systems, researchers develop maps that reveal important patterns in network flows. In practice, network flow models have implied memoryless first-order Markov chains, but recently researchers have introduced higher-order Markov chain models with memory to capture patterns in multi-step pathways. Higher-order models are particularly important for effectively revealing actual, overlapping community structure, but higher-order Markov chain models suffer from the curse of dimensionality: their vast parameter spaces require exponentially increasing data to avoid overfitting and therefore make mapping inefficient already for moderate-sized systems. To overcome this problem, we introduce an efficient cross-validated mapping approach based on network flows modeled by sparse Markov chains. To illustrate our approach, we present a map of citation flows in science with research fields that overlap in multidisciplinary journals. Compared with currently used categories in science of science studies, the research fields form better units of analysis because the map more effectively captures how ideas flow through science.

Keywords [en]
higher-order networks, sparse memory networks
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:umu:diva-147658OAI: oai:DiVA.org:umu-147658DiVA, id: diva2:1205313
Available from: 2018-05-14 Created: 2018-05-14 Last updated: 2018-06-09
In thesis
1. Toward higher-order network models
Open this publication in new window or tab >>Toward higher-order network models
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Complex systems play an essential role in our daily lives. These systems consist of many connected components that interact with each other. Consider, for example, society with billions of collaborating individuals, the stock market with numerous buyers and sellers that trade equities, or communication infrastructures with billions of phones, computers and satellites.

The key to understanding complex systems is to understand the interaction patterns between their components - their networks. To create the network, we need data from the system and a model that organizes the given data in a network representation. Today's increasing availability of data and improved computational capacity for analyzing networks have created great opportunities for the network approach to further prosper. However, increasingly rich data also gives rise to new challenges that question the effectiveness of the conventional approach to modeling data as a network. In this thesis, we explore those challenges and provide methods for simplifying and highlighting important interaction patterns in network models that make use of richer data.

Using data from real-world complex systems, we first show that conventional network modeling can provide valuable insights about the function of the underlying system. To explore the impact of using richer data in the network representation, we then expand the analysis for higher-order models of networks and show why we need to go beyond conventional models when there is data that allows us to do so. In addition, we also present a new framework for higher-order network modeling and analysis. We find that network models that capture richer data can provide more accurate representations of many real-world complex systems.

Place, publisher, year, edition, pages
Umeå: Umeå University, 2018. p. 89
Keywords
network science, complex systems, complex networks, network analysis, higher-order networks, community detection, citation networks, network modeling
National Category
Physical Sciences Other Computer and Information Science
Research subject
Physics
Identifiers
urn:nbn:se:umu:diva-147673 (URN)978-91-7601-892-7 (ISBN)
Public defence
2018-06-08, Sal N420, Naturvetarhuset, Umeå, 13:00 (English)
Opponent
Supervisors
Available from: 2018-05-18 Created: 2018-05-14 Last updated: 2018-06-11Bibliographically approved

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Bohlin, Ludvig

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Citation style
  • apa
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More languages
Output format
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