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On the Impact of Using Utilities Rather than Costs for Graph Matching

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Abstract

The concept of graph edit distance constitutes one of the most flexible graph matching paradigms available. The major drawback of graph edit distance, viz. the exponential time complexity, has been recently overcome by means of a reformulation of the edit distance problem to a linear sum assignment problem. However, the substantial speed up of the matching is also accompanied by an approximation error on the distances. Major contribution of this paper is the introduction of a transformation process in order to convert the underlying cost model into a utility model. The benefit of this transformation is that it enables the integration of additional information in the assignment process. We empirically confirm the positive effects of this transformation on five benchmark graph sets with respect to the accuracy and run time of a distance based classifier.

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Notes

  1. www.claymath.org/millennium-problems/p-vs-np-problem.

  2. 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.

  3. Applying the greedy assignment on utilities rather than costs means that we replace \(\underset{\forall j }{\arg \min }\) by \(\underset{\forall j }{\arg \max }\), of course.

  4. https://brunl01.users.greyc.fr/CHEMISTRY/index.html.

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Acknowledgements

This work has been supported by the Hasler Foundation Switzerland.

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Authors and Affiliations

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

    Kaspar Riesen

  2. Department of Informatics, University of Fribourg and HES-SO, 1700, Fribourg, Switzerland

    Andreas Fischer

  3. Institute of Computer Science, University of Bern, Neubrückstrasse 10, 3012, Bern, Switzerland

    Horst Bunke

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  1. Kaspar Riesen
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Correspondence to Kaspar Riesen.

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Riesen, K., Fischer, A. & Bunke, H. On the Impact of Using Utilities Rather than Costs for Graph Matching. Neural Process Lett 48, 691–707 (2018). https://doi.org/10.1007/s11063-017-9739-7

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