Contingency Structures and Concept Analysis

Formal Concept Analysis has found many uses in knowledge representation and data mining, but its penetration into established data-based research disciplines has been slower. Marrying application motivations, structures, and methods from epidemiology and the mathematical formalisms of FCA, we define Generalized Contingency Structures and Tagged Contingency Structures, two new objects that generalize the contingency table, an ad hoc data summarization device in epidemiology, to a mathematical object with well-understood structure. We have extended the FCA repertoire by adding to the Formal Context an associated structure that we call a Tag Context, which formally incorporates important kinds of background knowledge. We illustrate the motivation and use of these new ideas, formats, and objects with some brief examples.