Visual Detection of Structural Changes in Time-Varying Graphs Using Persistent Homology

Mustafa Hajij, Bei Wang, Carlos Eduardo Scheidegger, Paul Rosen

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we propose a novel method using persistent homology to quantify structural changes in time-varying graphs. Specifically, we transform each instance of the time-varying graph into a metric space, extract topological features using persistent homology, and compare those features over time. We provide a visualization that assists in time-varying graph exploration and helps to identify patterns of behavior within the data. To validate our approach, we conduct several case studies on real-world datasets and show how our method can find cyclic patterns, deviations from those patterns, and one-time events in time-varying graphs. We also examine whether a persistence-based similarity measure satisfies a set of well-established, desirable properties for graph metrics.

Original languageEnglish (US)
Title of host publicationProceedings - 2018 IEEE Pacific Visualization Symposium, PacificVis 2018
PublisherIEEE Computer Society
Pages125-134
Number of pages10
Volume2018-April
ISBN (Electronic)9781538614242
DOIs
StatePublished - May 25 2018
Event11th IEEE Pacific Visualization Symposium, PacificVis 2018 - Kobe, Japan
Duration: Apr 10 2018Apr 13 2018

Other

Other11th IEEE Pacific Visualization Symposium, PacificVis 2018
CountryJapan
CityKobe
Period4/10/184/13/18

Fingerprint

Data mining
Visualization

Keywords

  • event detection
  • graph drawing
  • graph timeline
  • graph visualization
  • persistent homology
  • topological data analysis

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Computer Vision and Pattern Recognition
  • Hardware and Architecture
  • Software

Cite this

Hajij, M., Wang, B., Scheidegger, C. E., & Rosen, P. (2018). Visual Detection of Structural Changes in Time-Varying Graphs Using Persistent Homology. In Proceedings - 2018 IEEE Pacific Visualization Symposium, PacificVis 2018 (Vol. 2018-April, pp. 125-134). IEEE Computer Society. https://doi.org/10.1109/PacificVis.2018.00024

Visual Detection of Structural Changes in Time-Varying Graphs Using Persistent Homology. / Hajij, Mustafa; Wang, Bei; Scheidegger, Carlos Eduardo; Rosen, Paul.

Proceedings - 2018 IEEE Pacific Visualization Symposium, PacificVis 2018. Vol. 2018-April IEEE Computer Society, 2018. p. 125-134.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Hajij, M, Wang, B, Scheidegger, CE & Rosen, P 2018, Visual Detection of Structural Changes in Time-Varying Graphs Using Persistent Homology. in Proceedings - 2018 IEEE Pacific Visualization Symposium, PacificVis 2018. vol. 2018-April, IEEE Computer Society, pp. 125-134, 11th IEEE Pacific Visualization Symposium, PacificVis 2018, Kobe, Japan, 4/10/18. https://doi.org/10.1109/PacificVis.2018.00024
Hajij M, Wang B, Scheidegger CE, Rosen P. Visual Detection of Structural Changes in Time-Varying Graphs Using Persistent Homology. In Proceedings - 2018 IEEE Pacific Visualization Symposium, PacificVis 2018. Vol. 2018-April. IEEE Computer Society. 2018. p. 125-134 https://doi.org/10.1109/PacificVis.2018.00024
Hajij, Mustafa ; Wang, Bei ; Scheidegger, Carlos Eduardo ; Rosen, Paul. / Visual Detection of Structural Changes in Time-Varying Graphs Using Persistent Homology. Proceedings - 2018 IEEE Pacific Visualization Symposium, PacificVis 2018. Vol. 2018-April IEEE Computer Society, 2018. pp. 125-134
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