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In this paper, we are revisiting pattern mining and especially itemsetmining, which allows one to analyze binary datasets in searching forinteresting and meaningful association rules and respective itemsets in anunsupervised way. While a summarization of a dataset based on a set of patternsdoes not provide a general and satisfying view over a dataset, we introduce aconcise representation -- the closure structure -- based on closed itemsets andtheir minimum generators, for capturing the intrinsic content of a dataset. Theclosure structure allows one to understand the topology of the dataset in thewhole and the inherent complexity of the data. We propose a formalization ofthe closure structure in terms of Formal Concept Analysis, which is welladapted to study this data topology. We present and demonstrate theoreticalresults, and as well, practical results using the GDPM algorithm. GDPM israther unique in its functionality as it returns a characterization of thetopology of a dataset in terms of complexity levels, highlighting the diversityand the distribution of the itemsets. Finally, a series of experiments showshow GDPM can be practically used and what can be expected from the output.

Discovery data topology with the closure structure. Theoretical and practical aspects