Social Network Analysis in Community-Built Databases - Community-Built Databases: Research and Development - page 67

3.3.1.1 After Reduction

Due to the high number of nodes and edges, many interesting groups and depen-
dencies are hard to find. Now we will try to reduce the formal context to lower
dimension and observe the changes. We have performed a reduction of the original
18 14 context to lower ranks and computed the corresponding concept lattices.

To illustrate, we have selected results obtained for rank 5 using the NMF method.
Modified context can be seen in the remaining part of Fig. 3.18 . A visualization of
the network into a bipartite graph (Fig. 3.17 ) reveals some changes, but is still too
complicated. The concept lattice can give us better insight. A detailed look at the
reduced lattice (Fig. 3.19 for rank 5) shows that the general layout has been
preserved, as well as the most important properties (e.g., mentioned implication
about Sylvia and Katherine). The reduction to rank 5 caused the merging of nodes
previously marked by attributes 10, 13, 14 (which we have discussed earlier).
To illustrate the amount of reduction, we can compute the similarity between the
original and the reduced context and draw Lorenz curves (see first row of Fig. 3.20 ).
A larger area under the curve means higher dissimilarity (lower similarity). Because
we compare the context using the object-by-object approach, we obtain several
curves (drawn using the gray color on the figure). To simplify the comparison, these
curves have been averaged (the result drawn using the black color). In the same
manner, we have computed these curves for formal concepts (second row of
Fig. 3.20 ).
An alternative approach to measuring the dimension reduction is to compute the
so-called normalized correlation dimension. For more details see [ 37 ] and [ 35 ].

Fig. 3.19 Concept lattice at rank 5