  In this paper we are interested in studying concise representations of
concepts and dependencies, i.e., implications and association rules. Such
representations are based on equivalence classes and their elements, i.e.,
minimal generators, minimum generators including keys and passkeys, proper
premises, and pseudo-intents. All these sets of attributes are significant and
well studied from the computational point of view, while their statistical
properties remain to be studied. This is the purpose of this paper to study
these singular attribute sets and in parallel to study how to evaluate the
complexity of a dataset from an FCA point of view. In the paper we analyze the
empirical distributions and the sizes of these particular attribute sets. In
addition we propose several measures of data complexity, such as
distributivity, linearity, size of concepts, size of minimum generators, for
the analysis of real-world and synthetic datasets.
