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Formal Concept Analysis of Attributed Networks

  • Henry Soldano
  • Guillaume Santini
  • Dominique Bouthinon
Chapter
Part of the Lecture Notes in Social Networks book series (LNSN)

Abstract

We consider attribute pattern mining in an attributed graph through recent developments of Formal Concept Analysis. The core idea is to restrain the extensional space, i.e., the space of possible pattern extensions in the vertex set O, to vertex subsets satisfying some topological property. We consider two levels. At the abstract level, we reduce the extension of each pattern in such a way that the corresponding abstract extension induces a subgraph whose nodes satisfy some connectivity property. At the local level a pattern has various extensions each associated with a connected component of the abstract subgraph associated with the pattern. We obtain that way abstract closed patterns and local closed patterns, together with abstract and local implications. Furthermore, working at abstract and local levels leads to proper interestingness measures that evaluate to what extent patterns and implications are related to the topological information. Finally, we relate local concepts to network communities and show that to plainly express such a notion it may be necessary to apply our methodology to a new graph derived from the original network. We consider in particular the detection and ordering of k-communities in subgraphs of an attributed network.

Keywords

Interior operators Attributed graphs Abstraction Closed patterns Communities 

Notes

Acknowledgements

This work was partially supported by CHIST-ERA grant (AdaLab, ANR 14-CHR2-0001-01).

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Henry Soldano
    • 1
    • 2
  • Guillaume Santini
    • 3
  • Dominique Bouthinon
    • 3
  1. 1.Université Paris 13VilletaneuseFrance
  2. 2.Museum National d’Histoire NaturelleISYEB - UMR 7205 CNRS MNHN UPMC EPHEParisFrance
  3. 3.Université Paris 13VilletaneuseFrance

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