Paper Info
Title
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 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 new light into Formal Concept Analysis from the point of view of the theory of linear operators over idempotent semimodules.
Year
DOI
Venue
2015
10.1007/978-3-319-19545-2_6
Lecture Notes in Artificial Intelligence
Field
DocType
Volume
Linear algebra,Discrete mathematics,Vector space,Algebra,Matrix (mathematics),Pure mathematics,Linear subspace,Semifield,Operator (computer programming),Linear map,Idempotence,Mathematics
Conference
9113
ISSN
Citations 
PageRank 
0302-9743
3
0.45
References 
Authors
4
2
Name
Order
Citations
PageRank
Francisco J. Valverde-Albacete111620.84
Carmen Peláez-moreno213022.07