Mapping Associations - Mapping Scientific Frontiers: The Quest for Knowledge Visualization - page 106

Pearson correlation coefficients can be calculated as follows, where X and Y are
data points in an N-dimensional space. X mean and Y mean are the mean of X and the
mean of Y, respectively.
X D x 1 x 2 :::

::: x N I Y D y 1 y 2 ::: ::: y N

The standard deviation of X, ¢ x , and that of Y, ¢ y , are defined as follows:

t t

N

i D 1 x i X mean 2
N 1

N

i D 1 y i Y mean 2
N 1

x D I y D

Finally, the standardized scores z x and z y are used to calculate the correlation
coefficient r xy , which in turn forms the correlation matrix.

X X mean
X

Y X mean
Y

z x D z y D

i D 1

N

z x z y

r xy D

N 1

Second, apply Pathfinder network scaling to the network defined by the correla-
tion matrix. Factor analysis is a standard practice in ACA. However, in traditional
ACA, MDS and factor analysis rarely appear in the same graphical representations.
In order to make knowledge visualizations clear and easy to interpret, we overlay
the intellectual groupings identified by factor analysis and the interconnectivity
structure modeled by the Pathfinder network scaling. Authors with similar colors
essentially belong to the same specialty and they should appear as a closely
connected group in the Pathfinder network. Therefore, one can expect to see the
two perspectives converge in the visualization. This is the third step.
Finally, display the citation impact of each author on top of the intellectual
groupings. The magnitude of the impact is represented by the height of a citation bar,
which in turn consists of a stack of color-coded annual citation sections. Figure 3.14
illustrates the construction of a three-dimensional knowledge landscape.
Figure 3.15 shows virtual landscape views of three different subject domains, the
upper middle one for computer graphics and applications (Chen and Paul 2001 ),
the lower left for hypertext (Chen 1999b ; Chen and Carr 1999a , b ), and the lower
right one for virtual reality. In the computer graphics example, we visualized author
co-citation patterns found in the journal IEEE Computer Graphics and Applications
(CG&A) between 1982 and 1999. The CG&A citation data include articles written
by 1,820 authors and co-authors. These authors cited a total of 10,292 unique
articles, written by 5,312 authors (first author only). Among them, 353 authors
who have received more than five citations in CG&A entered into author co-citation
analysis. Intellectual groupings of these 353 authors provide the basis for visualizing