Abstract
In data mining systems, which operate on complex data with structural relationships, graphs are often used to represent the basic objects under study. Yet, the high representational power of graphs is also accompanied by an increased complexity of the associated algorithms. Exact graph similarity or distance, for instance, can be computed in exponential time only. Recently, an algorithmic framework that allows graph dissimilarity computation in cubic time with respect to the number of nodes has been presented. This fast computation is at the expense, however, of generally overestimating the true distance. The present paper introduces six different post-processing algorithms that can be integrated in this suboptimal graph distance framework. These novel extensions aim at improving the overall distance quality while keeping the low computation time of the approximation. An experimental evaluation clearly shows that the proposed heuristics substantially reduce the overestimation in the existing approximation framework while the computation time remains remarkably low.
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Notes
- 1.
Similar notation is used for edges.
- 2.
BP stands for Bipartite. 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.
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Acknowledgements
This work has been supported by the Swiss National Science Foundation (SNSF) project Nr. 200021_153249, the Hasler Foundation Switzerland, and by the Spanish CICYT project DPI2013–42458–P and TIN2013–47245–C2–2–R.
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Ferrer, M., Serratosa, F., Riesen, K. (2015). Learning Heuristics to Reduce the Overestimation of Bipartite Graph Edit Distance Approximation. 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_2
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