The linear algebra in formal concept analysis over idempotent semifields

Abstract

We report on progress in characterizing K-valued FCA in algebraic terms, where K is an idempotent semifield. In this data mininginspired approach, incidences are matrices and sets of objects and attributes are vectors. The algebraization allows us to write matrixcalculus 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 new light into Formal Concept Analysis from the point of view of the theory of linear operators over idempotent semimodules.