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Efficient mining for structurally diverse subgraph patterns in large molecular databases


We present a new approach to large-scale graph mining based on so-called backbone refinement classes. The method efficiently mines tree-shaped subgraph descriptors under minimum frequency and significance constraints, using classes of fragments to reduce feature set size and running times. The classes are defined in terms of fragments sharing a common backbone. The method is able to optimize structural inter-feature entropy as opposed to purely occurrence-based criteria, which is characteristic for open or closed fragment mining. We first give an intuitive explanation why backbone refinement class features lead to a set of relevant features that are suitable for classification, in particular in the area of structure-activity relationships (SARs). We then show that backbone refinement classes yield a high compression in the search space of rooted perfect binary trees. We conduct several experiments to evaluate our theoretical insights in practice: A visualization suggests low co-occurrence and high entropy of backbone refinement class features. By comparison to a class of patterns sampled from the maximal patterns previously introduced by Al Hasan et al., we find a favorable tradeoff between the structural similarity and the resources needed to compute the descriptors. Cross-validation shows that classification accuracy is similar to the complete set of trees but significantly better than that of open trees, while feature set size is reduced by >90% and >30% compared to complete tree mining and open tree mining, respectively. Furthermore, compared to open or closed pattern mining, a large part of the search space can be pruned due to an improved statistical constraint (dynamic upper bound adjustment). This is confirmed experimentally by running times reduced by more than 60% compared to ordinary (static) upper bound pruning. The application of our method to the largest datasets that have been used in correlated graph mining so far indicates robustness against the minimum frequency parameter, and a cross-validation run on this data confirms that the novel descriptors render large training sets feasible, which previously might have been intractable.

A C++ implementation of the mining algorithm is available at Animated figures, links to datasets, and further resources are available at


  • Al Hasan, M., Chaoji, V., Salem, S., Besson, J., & Zaki, M. (2007). Origami: mining representative orthogonal graph patterns. In Seventh IEEE international conference on data mining (ICDM 2007) (pp. 153–162). Washington: IEEE Computer Society.

    Chapter  Google Scholar 

  • Benigni, R., & Bossa, C. (2008). Structure alerts for carcinogenicity, and the salmonella assay system: a novel insight through the chemical relational databases technology. Mutation Research/Reviews in Mutation Research, 659(3), 248–261.

    Article  Google Scholar 

  • Bringmann, B., Zimmermann, A., Raedt, L. D., & Nijssen, S. (2006). Don’t be afraid of simpler patterns. In Proceedings 10th PKDD (pp. 55–66). Berlin: Springer.

    Google Scholar 

  • Chi, Y., Muntz, R. R., Nijssen, S., & Kok, J. N. (2001). Frequent subtree mining—an overview.

  • Helma, C. (2006). Lazy structure-activity relationships (Lazar) for the prediction of rodent carcinogenicity and salmonella mutagenicity. In Molecular diversity (pp. 147–158).

  • Jahn, K., & Kramer, S. (2005). Optimizing gSpan for molecular datasets. In: Proceedings of the third international workshop on mining graphs, trees and sequences (MGTS-2005).

  • Kramer, S., De Raedt, L., & Helma, C. (2001). Molecular feature mining in HIV data. In KDD ’01: proceedings of the seventh ACM SIGKDD international conference on knowledge discovery and data mining (pp. 136–143). New York: ACM.

    Chapter  Google Scholar 

  • Maunz, A., Helma, C., & Kramer, S. (2009). Large-scale graph mining using backbone refinement classes. In KDD ’09: proceedings of the 15th ACM SIGKDD international conference on knowledge discovery and data mining (pp. 617–626). New York: ACM.

    Chapter  Google Scholar 

  • Morishita, S., & Sese, J. (2000). Traversing itemset lattice with statistical metric pruning. In Proceedings of the 19th ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems (pp. 226–236). New York: ACM.

    Google Scholar 

  • Nijssen, S., & Kok, J. N. (2004). A quickstart in frequent structure mining can make a difference. In KDD ’04: proceedings of the tenth ACM SIGKDD international conference on knowledge discovery and data mining (pp. 647–652). New York: ACM.

    Chapter  Google Scholar 

  • Nijssen, S., & Kok, J. N. (2006). Frequent subgraph miners: runtime don’t say everything. In Proceedings of the international workshop on mining and learning with graphs (MLG 2006) (pp. 173–180). Berlin, Germany.

  • OpenTox: A predictive toxicology framework. See also: Hardy, B., Douglas, N., Helma, C., et al.: Collaborative development of predictive toxicology applications fifth international symposium on computational methods in toxicology and pharmacology integrating internet resources (CMTPI 2009) (to appear). London: Taylor & Francis.

  • Rückert, U., & Kramer, S. (2007). Optimizing feature sets for structured data. In Proceedings of the 18th European conference on machine learning (ECML07) (pp. 716–723). Berlin: Springer-Verlag.

    Google Scholar 

  • Schulz, H., Kersting, C., & Karwath, A. ILP, the blind, and the elephant: Euclidean embedding of co-proven queries. In 19th international conference on inductive logic programming (ILP 2009).

  • Székely, L., & Wang, H. (2005). On subtrees of trees. Advances in Applied Mathematics, 34(1), 138–155. doi:10.1016/j.aam.2004.07.002.

    Article  MATH  MathSciNet  Google Scholar 

  • Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics Bulletin, 1(6), 80–83.

    Article  Google Scholar 

  • Wörlein, M., Meinl, T., Fischer, I., & Philippsen, M. (2005). A quantitative comparison of the subgraph miners MoFa, gSpan, ffsm, and Gaston. In Proceedings of PKDD (pp. 392–403). Berlin: Springer-Verlag.

    Google Scholar 

  • Yan, X., & Han, J. (2002). gSpan: graph-based substructure pattern mining. In ICDM ’02: proceedings of the 2002 IEEE international conference on data mining (ICDM’02) (p. 721). Washington: IEEE Computer Society.

    Google Scholar 

  • Yan, X., & Han, J. (2003). Closegraph: mining closed frequent graph patterns. In KDD ’03: proceedings of the ninth ACM SIGKDD international conference on knowledge discovery and data mining (pp. 286–295). New York: ACM.

    Chapter  Google Scholar 

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Correspondence to Andreas Maunz.

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Editors: Hendrik Blockeel, Karsten Borgwardt, and Xifeng Yan.

This research was supported by the EU seventh framework programme under contract No. Health-F5-2008-200787 (OpenTox 2009).

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Maunz, A., Helma, C. & Kramer, S. Efficient mining for structurally diverse subgraph patterns in large molecular databases. Mach Learn 83, 193–218 (2011).

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  • Correlated graph mining
  • Backbone
  • Dynamic upper bound pruning
  • Structural diversity