Assume that AL={??©A1, l1i???,...,??©Aj,
ljm???, ...} is a given pattern of the rollup (i.e., level climbing), where ??©Aj, ljm??? means the
hierarchy attached to attribute j is to be climbed from the current level to a higher
level ljm. The size of AL represents the maximal number of attributes for which the
attribute hierarchy needs to be explored bottom up, and hence |AL|= |P|. The operation
Rollup(L, P, AL) uses the lattice L as input to produce a new concept lattice
in which the attributes in P are either replaced with more general ones or ignored.
When ljm = ?‚• for a given attribute Aj, this means that attribute Aj is temporarily
discarded from analysis.
Like in data cubes, the rollup operation reduces the output set while the drill-down
operation increases the size of the output. Therefore, the lattice resulting from a
rollup is smaller than the initial one.
The algebraic representation of Rollup(L, P, AL) using the projection and assembly
is as follows:
Rollup(L, P, AL) = ) ( ) ( 1 L L P A ?— ? ??’ , where L and L1 correspond to B(O, A, R) and
B(O, A1, R1) respectively, and A1 is the set of |P| attributes generalized according
to the pattern AL.
Example:.Figure 3 illustrates a rollup of lattice L1 (see Figure 2) upon
an attribute by climbing up the hierarchy from the level containing c and
d to a higher level containing k.
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