Formal Context Transforms and Their Affordances for Exploratory Data Analysis

Abstract

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 is an element of G x 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.