Machine Learning

, Volume 83, Issue 2, pp 193–218 | Cite as

Efficient mining for structurally diverse subgraph patterns in large molecular databases

  • Andreas MaunzEmail author
  • Christoph Helma
  • Stefan Kramer


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


Correlated graph mining Backbone Dynamic upper bound pruning Structural diversity 


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Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Machine Learning LabUniversität FreiburgFreiburg i. Br.Germany
  2. ToxicologyBaselSwitzerland
  3. 3.Institut für Informatik/I12Garching b. MünchenGermany

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