Mapping Associations - Mapping Scientific Frontiers: The Quest for Knowledge Visualization - page 121

“master” space. The main output of an INDSCAL analysis is a group space in
which the stimuli, or objects, are depicted as points. In this example, six areas of
a city appear as points in the group space. The configuration of objects in this
group space is in effect a compromise between different individual's configurations.
Therefore the configuration may not be identical to the configuration of any
particular individual.
The INDSCAL also generates a subject space that represents each individual as a
point. Recall that the INDSCAL assumes a systematic distortion from an individual,
the position of an individual in the subject space reflects the “weights” which the
individual assigns to each dimension, just like a home buyer would give more
weights on the price dimension. Unlike with factor analysis and multidimensional
scaling, INDSCAL produces a unique orientation of the dimensions of the group
space. It is not legitimate to rotate the axes of a group space to a more meaningful
orientation. Furthermore, each point in the subject space should be interpreted as a
vector drawn from the origin. The length of this vector is roughly interpretable as
the proportion of the variance in the subject's data accounted for by the INDSCAL
solution. All subjects whose weights are in the same ratio will have vectors oriented
in the same direction. The appropriate measure for comparing subjects' weights is
the angle of separation between their vectors.
In Helm's study ( 1964 ), the observations of subject with normal color sight
mapped as a circle corresponding to the color wheel, with the orthogonal axes of the
two-dimensional map anchored by red and green and by blue and yellow, whereas
color-blind subjects' observations mapped as ellipses - they did not consider the
red-green (or blue-yellow) information as strongly when making color-matching
decisions. Figure 3.32 shows two red-green color-deficient subjects' individual
differences scaling results.
Figures 3.33 and 3.34 show SCI and SSCI weighted INSCAL displays, re-
spectively (Morris and McCain 1998 ). Contributors to SCI indexed journals and
those to SSCI indexed journals have different preferences and different levels
of granularity. If journals are wide spread along one dimension, it implies that
the corresponding subject fields have more sophisticated knowledge for scientists
to make finer distinctions. If journals are concentrated within a relatively small
range of a dimension, then it suggests that corresponding knowledge domains have
distinguished to a less extent.

3.3.4 Linear Approximation - Isomap

Scientists in many fields face the problem of simplifying high-dimensional data
by finding low-dimensional structure in it. MDS aims to map a given set of
high-dimensional data points into a low-dimensional space. The Isomap algorithm
(Tenenbaum et al. 2000 ) and the locally linear embedding (LLE) algorithm (Roweis
and Saul 2000 ) provide demonstrated improvements in dimensionality reduction.
Both were featured in the December 2000 issue of Science .