Thoughts on Exploiting Instability in Lattices for Assessing the Discrimination Adequacy of a Taxonomy

Conventionally in formal concept analysis (FCA), concept stability is preferred in the lattice, because instability (i.e. low stability) represents noise that clouds the analysis of the data. High stability means there are many objects with the same intent or many attributes with the same extent, which could be interpreted as redundant or absent objects or attributes. The differences between redundancy or absence need to be assessed quantitatively, a process that could be described as stability exploration. We have used FCA to analyse different taxonomies for user-generated content. For example, redundancy amongst attributes represents taxonomy classes unable to differentiate adequately the objects being classified. Absent attributes, redundant objects and absent objects can have various implications. Hence, instability in a lattice is desirable for some types of analysis.

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