  Until a present, the majority of work in data mining were interested in the
extraction of the frequent itemsets and the generation of the frequent
association rules from these itemsets. Sometimes, the frequent of associations
rules can revealed not-interesting in the direction where a frequent behavior
is in general a normal behavior in the database. These last years, some work
was focused on the exploitation and the extraction of rare itemset and shows
them interest. However, the very important size of those itemset was the
handicap of algorithms that exploit the rare pattern. In order to relieve this
problem, the present report proposes two exact concise representations of the
rare itemset, one based on the minimal generators and the other based on the
closed itemset. In this context, we introduce two new algorithms called GMRare
and MFRare which extract these two exact concise representations.
