Trees in Concept Lattices
Modeling Decisions for Artificial Intelligence, Springer, (2007)Abstract
The paper presents theorems characterizing concept lattices which
happen to be trees after removing the bottom element. Concept lattices
are the clustering/classification systems provided as an output of
formal concept analysis. In general, a concept lattice may contain
overlapping clusters and need not be a tree. On the other hand, tree-
like classification schemes are appealing and are produced by several
classification methods as the output. This paper attempts to help
establish a bridge between concept lattices and tree-based
classification methods. We present results presenting conditions for
input data which are sufficient and necessary for the output concept
lattice to form a tree after one removes its bottom element. In
addition, we present illustrative examples and several remarks on
related efforts and future research topics. 1