Trees in Concept Lattices
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.
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