Compressed pseudo-lattices

This paper introduces the notion of a compressed pseudo-lattice and suggests its use as a data structure in areas of application related to Formal Concept Analysis. It is closely related to the line diagram of a lattice and its use as a computational tool in applications such as machine learning, information retrieval and knowledge discovery in databases is discussed. The data structure—essentially a bipartite graph that incorporates an embedded sublattice—combines desirable features of concept lattices in a structure that allows for a flexible mechanism of scaling the size of the embedded sublattice, using defined operations that compress and expand it by removing or adding atoms and coatoms. A compressed pseudo-lattice essentially represents a complete sublattice from which a number of atoms and/or coatoms have been removed. Additionally the relation of the sublattice to the context from which it was derived is preserved. An application-dependent compression strategy or criterion is required to guide this process. The intent operations of a lattice are defined as substitutes for the infimum and supremum operations in compressed pseudo-lattices. It is argued that the removal of concepts from a concept lattice may hold advantages over traditional approaches.