relational tables) exists (takes its value)
in an independent way from the rest of items (attributes). Based on that fact, we
revisit the notion of itemset and association rule by imposing additional constraints
on them in order to make them more meaningful in a multidimensional context.
Two cases will be considered:
262 Missaoui, Jatteau, Boujenoui, & Naouali
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??? The cube C=
has a unique measure in M, which corresponds to a
COUNT aggregate function
??? The cube has at least a measure related to an aggregate function other than
COUNT
In the first case, ARM from a given cube C whose dimensions are in D amounts to
ARM from (a possibly subset of) the relational table T that generated C. However,
support and confidence of rules need to rely on the support of each fact in C, that
is, the number of individual records in T that support the fact. In the second case,
we first need to impose constraints on the structure of frequent itemsets and rules
so that the data mining output is meaningful. Then, a careful evaluation and interpretation
of such output is needed because any reference to a given measure value
must be expressed in terms of all the dimensions involved in the cube.
Frequent Closed Itemsets
Let C= be a data cube, where D is a set of dimensions involved in C, and
M a set of measures associated with D.
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