A methodology for analysis of concept lattice reduction

Formal concept analysis (FCA) is a mathematical theory of data analysis with applications in many areas. The problem of obtaining a concept lattice of an appropriate size was identified in several applications as one of the most important problems of FCA. In order to deal with this problem several techniques with different characteristics were proposed for concept lattice reduction. However, there are currently no adequate methods to assess what types of knowledge transformations can result from a reduction. A methodology for analysis of concept lattice reduction is presented here. It is based on the use of sets of proper implications holding in the original and reduced formal contexts or concept lattices. Working with both sets of implications, the methodology is able to show what is preserved, eliminated, inserted or transformed by a reduction technique. Three classes of reduction techniques are analyzed from the standpoint of the methodology in order to highlight techniques of each class have in common with respect to the transformations performed. Such analysis is followed by specific examples in each class.