Formal Context Transforms and Their Affordances for Exploratory Data Analysis

Consider a formal context (G, M, I) as the basic mechanism to capture information about a
set G of objects, a set M of attributes and the relation I ∈ G × M between them. Traditional
use of Formal Concept Analysis has some shortcomings in its information-eliciting capabilities,
which were expanded by the related processes of Formal Independence Analysis
and Formal Equivalence Analysis, which analyse different information types. The core
of these three approaches can be seen as different instantiations of a theorem by Birkhoff
when applied to different concept-forming operators (technically, some types of Galois
connection). In this paper, we propose the notion of context transform as a way to elicit
new information types from contexts that we call information qualia. We apply this notion
of context transform to explain how we may expect other formal analyses of different
information qualia to arise from a formal context. We also use the concept of formal quale
across the board to provide the affordances of many of the choices needed for practitioners
to make effective use of data analysis techniques.