Machine Learning

, Volume 82, Issue 2, pp 95–121 | Cite as

Efficiently mining δ-tolerance closed frequent subgraphs

  • Ichigaku Takigawa
  • Hiroshi Mamitsuka
Open Access


The output of frequent pattern mining is a huge number of frequent patterns, which are very redundant, causing a serious problem in understandability. We focus on mining frequent subgraphs for which well-considered approaches to reduce the redundancy are limited because of the complex nature of graphs. Two known, standard solutions are closed and maximal frequent subgraphs, but closed frequent subgraphs are still redundant and maximal frequent subgraphs are too specific. A more promising solution is δ-tolerance closed frequent subgraphs, which decrease monotonically in δ, being equal to maximal frequent subgraphs and closed frequent subgraphs for δ=0 and 1, respectively. However, the current algorithm for mining δ-tolerance closed frequent subgraphs is a naive, two-step approach in which frequent subgraphs are all enumerated and then sifted according to δ-tolerance closedness. We propose an efficient algorithm based on the idea of “reverse-search” by which the completeness of enumeration is guaranteed and for which new pruning conditions are incorporated. We empirically demonstrate that our approach significantly reduced the amount of real computation time of two compared algorithms for mining δ-tolerance closed frequent subgraphs, being pronounced more for practical settings.


Frequent subgraph mining δ-tolerance closedness Partial reverse search 


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Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Bioinformatics Center, Institute for Chemical ResearchKyoto UniversityUjiJapan
  2. 2.Institute for Bioinformatics Research and Development, BIRDJapan Science and Technology Agency, JSTTokyoJapan

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