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Spectral Measures of Distortion for Change Detection in Dynamic Graphs

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Complex Networks and Their Applications VII (COMPLEX NETWORKS 2018)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 813))

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Abstract

We propose a novel framework for detecting, quantifying and visualizing changes between two snapshots of a dynamic network. Unlike existing approaches, which can be sensitive to minor and isolated changes, and are often based on heuristics, we show how a theoretically-justified, inherently multi-scale notion of change, or distortion, can be defined and computed using spectral graph-theoretic tools. Our primary observation is that informative, robust and multi-scale measures of change can be obtained by computing a real-valued function (which we call the distortion function) on the nodes of the input graph, via the optimization of a pre-defined distortion energy in a provably optimal way. Based on extensive tests on a wide variety of networks, we demonstrate the ability of our approach to highlight the evolution of the network in an informative and multi-scale manner.

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Notes

  1. 1.

    The raw data is available at https://www.eecs.wsu.edu/~yyao/StreamingGraphs.html.

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Acknowledgements

Parts of this work were supported by the Jean Marjoulet chair from Ecole Polytechnique, a Google Focused Research Award, the ERC Starting Grant No. 758800 (EXPROTEA) and the French ANR GATO (ANR-16-CE40-0009-01).

Author information

Authors and Affiliations

  1. LIX, Ecole Polytechnique, Palaiseau, France

    Luca Castelli Aleardi & Maks Ovsjanikov

  2. University of Waterloo, Waterloo, Canada

    Semih Salihoglu

  3. Max Planck Institute for Informatics, Saarbrücken, Germany

    Gurprit Singh

Authors
  1. Luca Castelli Aleardi
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  2. Semih Salihoglu
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  3. Gurprit Singh
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  4. Maks Ovsjanikov
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Corresponding author

Correspondence to Luca Castelli Aleardi .

Editor information

Editors and Affiliations

  1. Nokia Bell Labs, Cambridge, UK

    Luca Maria Aiello

  2. IUT Lumière, University of Lyon, Bron Cedex, France

    Chantal Cherifi

  3. LE2I UMR CNRS 6306 9, University of Burgundy, Dijon Cedex, France

    Hocine Cherifi

  4. Mathematical Institute, University of Oxford, Oxford, UK

    Renaud Lambiotte

  5. Department of Computer Science and Technology, The Computer Laboratory, University of Cambridge, Cambridge, UK

    Pietro Lió

  6. Center for Complex Networks and Systems Research, School of Informatics, Computing, and Engineering, Indiana University, Bloomington, IN, USA

    Luis M. Rocha

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Castelli Aleardi, L., Salihoglu, S., Singh, G., Ovsjanikov, M. (2019). Spectral Measures of Distortion for Change Detection in Dynamic Graphs. In: Aiello, L., Cherifi, C., Cherifi, H., Lambiotte, R., Lió, P., Rocha, L. (eds) Complex Networks and Their Applications VII. COMPLEX NETWORKS 2018. Studies in Computational Intelligence, vol 813. Springer, Cham. https://doi.org/10.1007/978-3-030-05414-4_5

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