K-Formal Concept Analysis as linear algebra over idempotent semifields Articles uri icon

publication date

  • October 2018

start page

  • 579

end page

  • 603

volume

  • 467

International Standard Serial Number (ISSN)

  • 0020-0255

Electronic International Standard Serial Number (EISSN)

  • 1872-6291

abstract

  • We report on progress in characterizing K-valued FCA in algebraic terms, where K is an idempotent semifield. In this data mining-inspired approach, incidences are matrices and sets of objects and attributes are vectors. The algebraization allows us to write matrix calculus formulae describing the polars and the fixpoint equations for extents and intents. Adopting also the point of view of the theory of linear operators between vector spaces we explore the similarities and differences of the idempotent semimodules of extents and intents with the subspaces related to a linear operator in standard algebra. This allows us to shed some light into Formal Concept Analysis from the point of view of the theory of linear operators over idempotent semimodules. In the opposite direction, we state the importance of FCA-related concepts for dual order homomorphisms of linear spaces over idempotent semifields, specially congruences, the lattices of extents, intents and formal concepts. (C) 2018 Elsevier Inc. All rights reserved.

keywords

  • generalised formal concept analysis; concept lattice; neighborhood lattice; idempotent semiring; dioid; confusion matrix