7.1 Evaluation of the Frequentness Probabil-
Active Itemsets Queue (AIQ) that is initialized with all one-
item sets. The AIQ is sorted by frequentness probability
ity Calculations
in descending order. Without loss of generality, itemsets
We evaluated our frequentness probability calculation meth-
are represented in lexiographical order to avoid generating
ods on several artificial datasets with varying database sizes
them more than once. In each iteration of the algorithm,
|T | and densities. The density of an item denotes the ex-
i.e. each call of the getNext()-function, the first itemset X
pected number of transactions in which an item may be
in the queue is removed. X is the next most probable fre-
present (i.e. where its existence probability is in (0, 1]).
quent itemset because all other itemsets in the AIQ have
The probabilities themselves were drawn from a uniform
a lower frequentness probability due to the order on AIQ,
distribution. Note that the density is directly related to
and all of X’s supersets (which have not yet been gener-
the degree of uncertainty. If not stated otherwise, we used a
ated) cannot have a higher frequentness probability due to
database consisting of 10, 000 to 10, 000, 000 uncertain trans-
Lemma 17. Before X is returned to the user, it is refined
actions and a density of 0.5. The frequentness probability
in a candidate generation step. In this step, we create all
threshold τ of was set to 0.9.
supersets of X obtained by adding single items x to the end
We use the following notations for our frequentness prob-
of X, in such a way that the lexiographical order of X ∪ x
ability algorithms: Basic: basic probability computation
is maintained. These are then added to the AIQ after their
(Section 3.2), Dynamic: dynamic probability computation
respective frequentness probabilities are computed (Section
(Section 4.1), Dynamic+P: dynamic probability compu-
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