Group Theoretical Structures for Representing Data Contexts

Data contexts, which describe the relation between objects, attributes, and attribute values, can often be described advantageously by algebraic structures. In this contribution, a representation of data contexts by finite abelian groups will be discussed. For this representation, a framework is given by contexts which have the elements of a group as objects (which label the rows of the data table or context), the elements of its character group as attributes (which label the columns), and the elements of the complex unit circle as attribute values (these label the entries in the cells of the data table). The non-empty extents of the appropriately scaled context are exactly the subgroups and their cosets. For the analysis of data, it is important to examine which data contexts are isomorphic to or can be embedded into such group contexts. This will be explained by some examples, in particular taken from the field of experimental designs.