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A Formal Concept Analysis Look at the Analysis of Affiliation Networks

  • Francisco J. Valverde-AlbaceteEmail author
  • Carmen Peláez-Moreno
Chapter
Part of the Lecture Notes in Social Networks book series (LNSN)

Abstract

In this paper we try to analyse the dual-projection approach to weighted 2-mode networks using the tools of\(\mathcal{K}\)-Formal Concept Analysis (\(\mathcal{K}\)-FCA), an extension of FCA for incidences with values in a particular kind of semiring.

For this purpose, we first revisit the isomorphisms between 2-mode networks with formal contexts. In the quest for similar relations when the networks have non-Boolean weights, we relate the dual-projection method to both the Singular Value Decomposition and the Eigenvalue Problem of matrices with values in such algebras, as embodied in Kleinberg’s Hubs and Authorities (HITS) algorithm.

To recover a relation with multi-valued extensions of FCA, we introduce extensions of the HITS algorithm to calculate the influence of nodes in a network whose adjacency matrix takes values over dioids, zerosumfree semirings with a natural order. In this way, we show the original HITS algorithm to be a particular instance of the generic construction, but also the advantages of working in idempotent semifields, instances of dioids.

Subsequently, we also make some connections with extended\(\mathcal{K}\)-FCA, where the particular kind of dioid is an idempotent semifield, and provide theoretical reasoning and evidence that the type of knowledge extracted from a matrix by one procedure and the other are different.

Keywords

Weighted two-mode networks Dual-projection analysis HITS SVD Idempotent semifield Idempotent Formal Concept Analysis Idempotent HITS 

Notes

Acknowledgements

The authors have been partially supported by the Spanish Government-MinECo projects TEC2014-53390-P and TEC2014-61729-EXP for this work.

We would like to thank the reviewers of earlier versions of this paper for their help in improving it.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Francisco J. Valverde-Albacete
    • 1
    Email author
  • Carmen Peláez-Moreno
    • 1
  1. 1.Department of Signal Theory and CommunicationsUniversidad Carlos III de MadridLeganésSpain

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