▁the ▁candidate ▁sets ▁from ▁the ▁large ▁item ▁sets ▁of ▁the ▁preceding ▁level , ▁he eding ▁the ▁down ward ▁closure ▁lemma . ▁ ▁access es ▁a ▁field ▁of ▁the ▁data ▁structure ▁that ▁represents ▁candidate ▁set ▁, ▁which ▁is ▁initially ▁assumed ▁to ▁be ▁zero . ▁Many ▁details ▁are ▁omitted ▁below , ▁usually ▁the ▁most ▁important ▁part ▁of ▁the ▁implementation ▁is ▁the ▁data ▁structure ▁used ▁for ▁storing ▁the ▁candidate ▁sets , ▁and ▁counting ▁their ▁frequencies . ▁ ▁Ex amples ▁ ▁Example ▁ 1 ▁▁ ▁Consider ▁the ▁following ▁database , ▁where ▁each ▁row ▁is ▁a ▁transaction ▁and ▁each ▁cell ▁is ▁an ▁individual ▁item ▁of ▁the ▁transaction : ▁ ▁The ▁association ▁rules ▁that ▁can ▁be ▁determined ▁from ▁this ▁database ▁are ▁the ▁following : ▁▁▁ 1 0 0 % ▁of ▁sets ▁with ▁alpha ▁also ▁contain ▁beta ▁▁ 5 0 % ▁of ▁sets ▁with ▁alpha , ▁beta ▁also ▁have ▁e psilon ▁▁ 5 0 % ▁of ▁sets ▁with ▁alpha , ▁beta ▁also ▁have ▁the ta ▁ ▁we ▁can ▁also ▁illustrate ▁this ▁through ▁a ▁variety ▁of ▁examples . ▁ ▁Example ▁ 2 ▁▁ ▁Assume ▁that ▁a ▁large ▁super market ▁tracks ▁sales ▁data ▁by ▁stock - keep ing ▁unit ▁( SK U ) ▁for ▁each ▁item : ▁each ▁item , ▁such ▁as ▁" but ter " ▁or ▁" b read ", ▁is ▁identified ▁by ▁a ▁numerical ▁SK U . ▁The ▁super market ▁has ▁a ▁database ▁of ▁transactions ▁where ▁each ▁transaction ▁is ▁a ▁set ▁of ▁SK Us ▁that ▁were ▁bought ▁together . ▁ ▁Let ▁the ▁database ▁of ▁transactions ▁consist ▁of ▁following ▁item sets