  In this paper, we are revisiting pattern mining and especially itemset
mining, which allows one to analyze binary datasets in searching for
interesting and meaningful association rules and respective itemsets in an
unsupervised way. While a summarization of a dataset based on a set of patterns
does not provide a general and satisfying view over a dataset, we introduce a
concise representation -- the closure structure -- based on closed itemsets and
their minimum generators, for capturing the intrinsic content of a dataset. The
closure structure allows one to understand the topology of the dataset in the
whole and the inherent complexity of the data. We propose a formalization of
the closure structure in terms of Formal Concept Analysis, which is well
adapted to study this data topology. We present and demonstrate theoretical
results, and as well, practical results using the GDPM algorithm. GDPM is
rather unique in its functionality as it returns a characterization of the
topology of a dataset in terms of complexity levels, highlighting the diversity
and the distribution of the itemsets. Finally, a series of experiments shows
how GDPM can be practically used and what can be expected from the output.
