Looking for a structural characterization of the sparseness measure of (frequent closed) itemset contexts

It is widely recognized that the performances of frequent-pattern mining algorithms are closely dependent on data being handled, i.e., sparse or dense. The same situation applies to the efficiency of concise representations of frequently occurring patterns with respect to the extraction task and the obtained compactness rates, as well as for other data mining techniques such as clustering, and for the mining algorithms of different pattern classes such as hypergraphs. In this paper, we raise a fundamental question: how can we formally define the sparseness of an arbitrary context and assess its value? As an answer, based on the framework of the succinct system of minimal generators, we present an innovative characterization of context sparseness, as well as a new sparseness measure which results from the aggregation of two complementary measures, namely the succinctness and compactness measures of each equivalence class, induced by the Galois closure operator. Experiments carried out mainly attain a finer classification of benchmark contexts and, then, confirm our viewpoint that the “dense” and “sparse” labels are not absolute.