The user can then go through
coarser/finer levels of data abstraction (i.e., rollup vs. drill-down) when an attribute
(or dimension) hierarchy is available (e.g., levels of company location are city, state,
and country), see a DM output under different perspectives (one or many attributes),
or use the dice operator to select some specific attributes (or attribute values) and/or
a set of objects. As a preliminary illustration, a rollup on a DM output in our running
example means either a reduction in the number of perspectives to consider
(e.g., financial features) or a generalization upon one or many perspectives (e.g.,
company location).
Based on the background provided earlier, we define a set of operators inspired
from OLAP techniques (e.g., drill-down, slice), which act like relational algebra
by operating on concept lattices to get new ones.
Operations.on.Lattices
In this subsection, we formally define three main operations on lattices: projection,
selection, and assembly. More details about theoretical results can be found in Ganter
and Wille (1999) and Valtchev et al. (2002a).
The projectioN of L = B(O, A, R) over A1 ??‚ A is given by the following mapping:
?•: L?†’L1= B(O, A1, R1).
Toward Integrating Data Warehousing with Data Mining Techniques 26
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