Mapping Associations - Mapping Scientific Frontiers: The Quest for Knowledge Visualization - page 95

Fig. 3.3 Nodes a and c are connected by two paths. If r D1 , Pat h 2 is longer than Pat h 1 ,
violating the triangle inequality; so it needs to be removed

links. Figure 3.3 illustrates how a link is removed if it violates the triangle inequality.
See (Chen 1999a , b ; Chen and Paul 2001 ; Schvaneveldt et al. 1989 ) for further
details.
The spatial layout of a Pathfinder network is determined by a force-directed
graph-drawing algorithm (Kamada and Kawai 1989 ). Because of its simplicity and
intuitive appealing, force-directed graph drawing becomes increasingly popular in
information visualization.
Typical applications of Pathfinder networks include modeling a network of
concepts based on similarity ratings given by human experts, constructing proce-
dural and protocol analysis models of complex activities such as air-traffic control,
and comparing learners' Pathfinder networks at various stages of their learning
(Schvaneveldt 1990 ).
Pathfinder networks display links between objects explicitly. Structural patterns
are easy for our perceptions to detect. In addition, Pathfinder network scaling is an
effective link-reduction mechanism, which prevents a network from being cluttered
by too many links. Figure 3.4 shows a Pathfinder network of 20 cities in the US.
The colors of nodes indicate the partition of the network based on the degree of
each node: white nodes have the degree of 3, blue nodes 2, and green nodes 1. The
size of each node indicates the centrality of the node. In this case, the Pathfinder
network turns out to be the unique minimum spanning tree. Figure 3.5 shows the
partition of the Pathfinder network by the degree of each node. The larger the size
of a node, the closer it is to the center.

3.2.3 Measuring the Similarity Between Images

Now we use an example from content-based image retrieval (CBIR) to illustrate
the use of Pathfinder and GSA (Chen et al. 2000 ). GSA is generic. Not only is it
suitable for text documents, but also can handle other types of entities in a similar
way. In the following example, we demonstrate how to derive a structure of images.
In addition, the structure of images provides additional insights to the quality of
similarity measures and characteristics of different feature extraction algorithms.