Mining Tree Patterns with Partially Injective Homomorphisms

  • Till Hendrik SchulzEmail author
  • Tamás Horváth
  • Pascal Welke
  • Stefan Wrobel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11052)


One of the main differences between inductive logic programming (ILP) and graph mining lies in the pattern matching operator applied: While it is mainly defined by relational homomorphism (i.e., subsumption) in ILP, subgraph isomorphism is the most common pattern matching operator in graph mining. Using the fact that subgraph isomorphisms are injective homomorphisms, we bridge the gap between ILP and graph mining by considering a natural transition from homomorphisms to subgraph isomorphisms that is defined by partially injective homomorphisms, i.e., which require injectivity only for subsets of the vertex pairs in the pattern. Utilizing positive complexity results on deciding homomorphisms from bounded tree-width graphs, we present an algorithm mining frequent trees from arbitrary graphs w.r.t. partially injective homomorphisms. Our experimental results show that the predictive performance of the patterns obtained is comparable to that of ordinary frequent subgraphs. Thus, by preserving much from the advantageous properties of homomorphisms and subgraph isomorphisms, our approach provides a trade-off between efficiency and predictive power.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Till Hendrik Schulz
    • 1
    Email author
  • Tamás Horváth
    • 1
    • 2
    • 3
  • Pascal Welke
    • 1
  • Stefan Wrobel
    • 1
    • 2
    • 3
  1. 1.Department of Computer ScienceUniversity of BonnBonnGermany
  2. 2.Fraunhofer IAIS, Schloss BirlinghovenSankt AugustinGermany
  3. 3.Fraunhofer Center for Machine LearningSankt AugustinGermany

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