The Structure and Dynamics of Scientific Knowledge - Mapping Scientific Frontiers: The Quest for Knowledge Visualization - page 184

Tabl e 5. 1 Comparisons of networks by the number of links, where K is
the number of unique edges in the graph
G D (Vertices, edges)

#Vertices #Eedges Example: N D 367

MDS N 0 0

MST N N 1 366

PF N 3N 398

Full matrix N N(N 1)/2 61,175

domain, our focus turned to the question of the functionality of such visualizations
and maps. It became clear that a more focused perspective is the key to a more
fruitful use of such visualizations. This is the reason we will turn to Thomas Kuhn's
puzzle-solving paradigms and focus on the scenarios of competing paradigms in
scientific frontiers in next chapter. Henry Small's specialty narrative also provides
an excellent example of how domain visualization can guide us to a greater access
to the core knowledge in scientific frontiers.

5.3.2.3 MDS, MST, and Pathfinder

Multidimensional scaling (MDS) maps are among the most widely used ones
to depict intellectual groupings. MDS-based maps are consistent with Gestalt
principles - our perceived groupings are largely determined by proximity, similarity,
and continuity. MDS is designed to optimize the match between pairwise proximity
and distance in high - dimensional space. In principle, MDS should place similar
objects next to each other in a two- or three-dimensional map and keep dissimilar
ones farther apart.
MDS is easily accessible in most statistical packages such as SPSS, SAS, and
Matlab. However, MDS provides no explicit grouping information. We have to judge
proximity patterns carefully in order to identify the underlying structure. Proximity-
based pattern recognition is not easy and sometimes can be misleading. For
example, one-dimensional MDS may not necessarily preserve a linear relationship.
A two-dimensional MDS configuration may not be consistent with the results of
hierarchical clustering algorithms - two points next to each other in an MDS
configuration may belong to different clusters. Finally, three-dimensional MDS may
become so visually complex that it is hard to make sense of it without rotating
the model in a 3D space and studying it from different angles. Because of these
limitations, researchers often choose to superimpose additional information over
an MDS configuration so as to clarify groupings of data points, for example, by
drawing explicit boundaries of point clusters in an MDS map. Most weaknesses of
MDS boil down to the lack of local details. If we treat an MDS as a graph, we can
easily compare the number of links across various network solutions and an MDS
configuration (See Table 5.1 ).
Figure 5.16 shows a minimum spanning tree (MST) of an author co-citation
network of 367 prominent authors in the field of hypertext. The original author
co-citation network consisted of 61,175 links among these authors. A fully