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Physics > Data Analysis, Statistics and Probability

arXiv:1807.07747 (physics)
[Submitted on 20 Jul 2018]

Title:Simplicial complexes and complex systems

Authors:Vsevolod Salnikov, Daniele Cassese, Renaud Lambiotte
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Abstract:We provide a short introduction to the field of topological data analysis and discuss its possible relevance for the study of complex systems. Topological data analysis provides a set of tools to characterise the shape of data, in terms of the presence of holes or cavities between the points. The methods, based on notion of simplicial complexes, generalise standard network tools by naturally allowing for many-body interactions and providing results robust under continuous deformations of the data. We present strengths and weaknesses of current methods, as well as a range of empirical studies relevant to the field of complex systems, before identifying future methodological challenges to help understand the emergence of collective phenomena.
Comments: 8 pages, 4 figures
Subjects: Data Analysis, Statistics and Probability (physics.data-an)
Cite as: arXiv:1807.07747 [physics.data-an]
  (or arXiv:1807.07747v1 [physics.data-an] for this version)
  https://doi.org/10.48550/arXiv.1807.07747
Related DOI: https://doi.org/10.1088/1361-6404/aae790

Submission history

From: Renaud Lambiotte [view email]
[v1] Fri, 20 Jul 2018 09:00:54 UTC (938 KB)
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