Galois Connections Between Semimodules and Applications in Data Mining

Abstract

In [1] a generalisation of Formal Concept Analysis was introduced with data mining applications in mind, $\mathcal K$ -Formal Concept Analysis, where incidences take values in certain kinds of semirings, instead of the standard Boolean carrier set. A fundamental result was missing there, namely the second half of the equivalent of the main theorem of Formal Concept Analysis. In this continuation we introduce the structural lattice of such generalised contexts, providing a limited equivalent to the main theorem of $\mathcal{K}$-Formal Concept Analysis which allows to interpret the standard version as a privileged case in yet another direction. We motivate our results by providing instances of their use to analyse the confusion matrices of multiple-input multiple-output classifiers.