Ordinal Motifs in Lattices

The foundation of any formal analysis of data is the identification of unique and meaningful substructures and properties. The realm of ordinal structures, in particular lattices, is no exemption to that. The field of Formal Conceptual Analysis (FCA), which derives lattices from data tables, called formal contexts, is already very well equipped with tools and notions for identifying and analyzing important substructures. One essential tool of FCA is to provide a user a lattice diagram of meaningful size, which can be interpreted (or even explained). For obvious reasons, this approach defies any applicability to data sets as they are commonly used today, as the resulting lattices are comprised of thousands of elements. In addition, the lattice diagram itself, as the primary means of communication, presents a significant hurdle to interpretation for untrained users. Common approaches tackle the first problem by data set reductions within the data tables [10, 14] or within the resulting lattice structure [1, 2, 9, 15].