The following algorithm exploits the properties defined in the section Operations
on Lattices to perform the assembly of two lattices L1 and L2. A simplistic way to
implement such operation is to compare each node in L1 with each node in L2. In
order to rapidly get real concepts, each one of the two lattices is explored in a bottom-
up way following a linear extension of the lattice order. The following procedure
presents a simplified description of the implemented algorithm where E stores the
intersection of two extents. If E is a new value, then it corresponds to the extent of
a new concept c. In that case, concept c is then created and linked to its immediate
predecessors (descendants). More details can be found in Valtchev et al. (2002a).
Algorithm.2: Assembly
Input: L1 = ??©G1, ?‰¤L1???, L2 = ??©G2, ?‰¤L2???
Output: L = ??©G, ?‰¤L???
L ?†? ??…
Sort(G1) according to a linear extension of ?‰¤L1;
Sort(G2) according to a linear extension of ?‰¤L2;
for.each ci in G1 do
for.each cj in G2 do
E ?†? extent(ci) ??© extent(cj)
Table 3. Trace of the projection of lattice L (Figure 1) on abcd
n i1 Successors Concept
1 abcd 5 no
5 abcd 7,10,12 yes
10 abc 15,17 yes
15 ab 19 yes
19 a NIL yes
17 ac 19 yes
7 acd 11 no
11 acd 14,17 yes
14 ad 19 yes
12 abd 13,15 yes
13 ad 14 no
Toward Integrating Data Warehousing with Data Mining Techniques 2
Copyright ?© 2007, Idea Group Inc.
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