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if.E does not exist as an extent of a newly computed concept then
.....c ?†? (E, intent(ci) ??? intent(cj))
L ?†? L ??? {c}
Link c to its immediate predecessors
return L
Another way to implement the assembly operation consists to start with L1 and iteratively
conduct as many assembly operations as there are attributes in L2.
Among the questions that we had to answer while exploring the projection and the
assembly operations, we enumerate the following:
??? Is it worthwhile to perform these operations on lattices rather than recomputing
lattices from scratch based on the projection or the apposition (i.e., horizontal
concatenation) of contexts?
??? Are there other benefits of these operations on lattices?
To answer the first question, we have conducted an experimental study which
showed that computing a projection on a lattice is generally more efficient than the
lattice construction using the modified context. The gain increases significantly as
the proportion of projection attributes augments. Figure 4 illustrates this fact for a
context of 500 objects and 50 attributes.
Our work on lattice assembly (Valtchev et al., 2002a) shows that this operation has
interesting empirical and theoretical performances. Furthermore, the other benefit
of the two operations lies in the fact that they can be used to construct a lattice in a
distributed or parallel environment, or construct a nested structure of the lattice, called
nested line diagram (see Visualization Mechanisms section for more details).
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