Lattices in machine learning: Complexity issues

Abstract. The use of a so-called concept lattice for deriving concepts from a given set of entities and attributes is examined. A number of variations are discussed including constrained, unconstrained and augmented concept lattices. Bounds for worst case behaviour, as well as conditions under which worst-case behaviour arises, are adduced. It is argued that worst-case behaviour is unlikely to arise in applications which are amenable to machine learning. Pruning is also mentioned as a means of keeping the lattice down to a tractable size.