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Comparing Temporal Graphs Using Dynamic Time Warping

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Complex Networks and Their Applications VIII (COMPLEX NETWORKS 2019)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 882))

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Abstract

The links between vertices within many real-world networks change over time. Correspondingly, there has been a recent boom in studying temporal graphs. Proximity-based pattern recognition in temporal graphs requires a (dis)similarity measure to compare different temporal graphs. To this end, we propose to employ dynamic time warping on temporal graphs. We define the dynamic temporal graph warping distance (dtgw) to determine the (dis)similarity of two temporal graphs. Our novel measure is flexible and can be applied in various application domains. We show that computing the dtgw-distance is a challenging (in general NP-hard) optimization problem and we identify some polynomial-time solvable special cases. Moreover, we develop an efficient heuristic which performs well in empirical studies. In experiments on real-word data we show that our dtgw-distance performs favorably in de-anonymizing networks compared to other approaches.

Full version available on arXiv (http://arxiv.org/abs/1810.06240).

B. Jain—Supported by the DFG project JA 2109/4-1.

M. Renken—Supported by the DFG project NI 369/17-1.

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Notes

  1. 1.

    The Exponential Time Hypothesis, an established concept in computational complexity theory, asserts that there is a constant \(c > 0\) such that 3-SAT cannot be solved in \(O(2^{cn})\) time, where n is the number of variables in the input formula [10].

  2. 2.

    In the full arXiv version we discuss several alternative initializations, all of which performed comparably well in experiments. Notably, initializing with a shortest warping path is the fastest initialization.

  3. 3.

    We also tested other signatures such as size of the connected component or betweenness centrality. However, the performance was (slightly) worse.

  4. 4.

    Source code available at www.akt.tu-berlin.de/menue/software.

  5. 5.

    Available as a Python module at www.https://github.com/src-d/lapjv.

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Authors and Affiliations

  1. Faculty IV, Algorithmics and Computational Complexity, TU Berlin, Berlin, Germany

    Vincent Froese, Rolf Niedermeier & Malte Renken

  2. Faculty IV, Distributed Artificial Intelligence Laboratory, TU Berlin, Berlin, Germany

    Brijnesh Jain

Authors
  1. Vincent Froese
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  2. Brijnesh Jain
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  3. Rolf Niedermeier
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  4. Malte Renken
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Corresponding author

Correspondence to Malte Renken .

Editor information

Editors and Affiliations

  1. University of Burgundy, Dijon Cedex, France

    Hocine Cherifi

  2. Università degli Studi di Milano, Milan, Italy

    Sabrina Gaito

  3. University of Aveiro, Aveiro, Portugal

    José Fernendo Mendes

  4. Universidad Carlos III de Madrid, Leganés, Madrid, Spain

    Esteban Moro

  5. Indiana University, Bloomington, IN, USA

    Luis Mateus Rocha

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Froese, V., Jain, B., Niedermeier, R., Renken, M. (2020). Comparing Temporal Graphs Using Dynamic Time Warping. In: Cherifi, H., Gaito, S., Mendes, J., Moro, E., Rocha, L. (eds) Complex Networks and Their Applications VIII. COMPLEX NETWORKS 2019. Studies in Computational Intelligence, vol 882. Springer, Cham. https://doi.org/10.1007/978-3-030-36683-4_38

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