g., nesting) based on the slice operation.
The algebraic representation of the slice operation is:
Slice(L, ai) = ? ai (L).
In our running example, Slice(L, Internal) will provide the lattice limited to the
dimension (attribute) Internal.
Dice
Dice(L, P, Q) limits the analysis to an arbitrary subset Q of objects and/or a subset
P of attributes. Here again, our definition of the dice operation in concept lattices
has a meaning relatively distinct from the dice operation in data cubes.
The algebraic representation of the dice operation is:
Dice(L, P, Q) =
)) ( ( L P i o Q ? ???
where Q ??‚ O and/or P ??‚ A.
Toward Integrating Data Warehousing with Data Mining Techniques 26
Copyright ?© 2007, Idea Group Inc. Copying or distributing in print or electronic forms without written permission
of Idea Group Inc. is prohibited.
For example, one would like to focus his/her analysis of the lattice L to companies
1, 2, and 3 using shareholding features only.
Algorithms
Now that the OLAP operations acting on DM output are formally defined using
operations on lattices, we describe hereafter algorithms for the implementation of
projection and assembly.
Algorithm 1 implements the projection and has two arguments: the attribute set P
to be projected on, and the node n which is initially set to the infimum (i.e., the bottom
of the lattice). It handles a traversal of the lattice in a recursive way from the
bottom to the top (supremum).
Pages:
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500