The intuition behind the concept is that given a
(closed) collection S of sets that are frequent, the negative
border contains the “closest” itemsets that could
be frequent, too. The candidate collections of the levelwise
algorithms are, in effect, the negative borders of
the collections of frequent sets found so far, and the
collection of all candidates that were not frequent is
the negative border of the collection of frequent sets.
Of particular importance is the fact that the negative
border needs to be evaluated, in order to be sure that
no frequent sets are missed [MT96].