Concept Lattice Simplification in Formal Concept Analysis Using Attribute Clustering

Abstract

In Formal Concept Analysis (FCA), a concept lattice graphically portrays the underlying relationships between the objects and attributes of an information system. One of the key complexity problems of concept lattices lies in extracting the useful information. The unorganized nature of attributes in huge contexts often does not yield an informative lattice in FCA. Moreover, understanding the collective relationships between attributes and objects in a larger many valued context is more complicated. In this paper, we introduce a novel approach for deducing a smaller and meaningful concept lattice from which excerpts of concepts can be inferred. In existing attribute-based concept lattice reduction methods for FCA, mostly either the attribute size or the context size is reduced. Our approach involves in organizing the attributes into clusters using their structural similarities and dissimilarities, which is commonly known as attribute clustering, to produce a derived context. We have observed that the deduced concept lattice inherits the structural relationship of the original one. Furthermore, we have mathematically proved that a unique surjective inclusion mapping from the original lattice to the deduced one exists.