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Greedy Graph Edit Distance

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Machine Learning and Data Mining in Pattern Recognition (MLDM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9166))

Abstract

In pattern recognition and data mining applications, where the underlying data is characterized by complex structural relationships, graphs are often used as a formalism for object representation. Yet, the high representational power and flexibility of graphs is accompanied by a significant increase of the complexity of many algorithms. For instance, exact computation of pairwise graph dissimilarity, i.e. distance, can be accomplished in exponential time complexity only. A previously introduced approximation framework reduces the problem of graph comparison to an instance of a linear sum assignment problem which allows graph dissimilarity computation in cubic time. The present paper introduces an extension of this approximation framework that runs in quadratic time. We empirically confirm the scalability of our extension with respect to the run time, and moreover show that the quadratic approximation leads to graph dissimilarities which are sufficiently accurate for graph based pattern classification.

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Notes

  1. 1.

    Note that QAPs are known to be \(\mathcal {NP}\) -complete, and therefore, an exact and efficient algorithm for the graph edit distance problem can not be developed unless \(\mathcal {P} = \mathcal {NP}\).

  2. 2.

    In [24] it is formally proven that this approximation scheme builds an upper bound of the exact graph edit distance.

  3. 3.

    The assignment problem can also be formulated as finding a matching in a complete bipartite graph and is therefore also referred to as bipartite graph matching problem.

  4. 4.

    www.iam.unibe.ch/fki/databases/iam-graph-database.

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Acknowledgements

This work has been supported by the Hasler Foundation Switzerland and the Swiss National Science Foundation project 200021_153249.

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Authors and Affiliations

  1. Institute for Information Systems, University of Applied Sciences and Arts Northwestern Switzerland, Riggenbachstrasse 16, 4600, Olten, Switzerland

    Kaspar Riesen, Miquel Ferrer & Rolf Dornberger

  2. Institute of Computer Science and Applied Mathematics, University of Bern, Neubrückstrasse 10, 3012, Bern, Switzerland

    Kaspar Riesen & Horst Bunke

Authors
  1. Kaspar Riesen
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  2. Miquel Ferrer
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  4. Horst Bunke
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Correspondence to Kaspar Riesen .

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  1. IBaI, Leipzig, Germany

    Petra Perner

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Riesen, K., Ferrer, M., Dornberger, R., Bunke, H. (2015). Greedy Graph Edit Distance. In: Perner, P. (eds) Machine Learning and Data Mining in Pattern Recognition. MLDM 2015. Lecture Notes in Computer Science(), vol 9166. Springer, Cham. https://doi.org/10.1007/978-3-319-21024-7_1

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  • DOI: https://doi.org/10.1007/978-3-319-21024-7_1

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