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2.3 Data Visualization 59

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Figure 2.13 Visualization of a 2-D data set using a scatter plot. Source: www.cs.sfu.ca/jpei/publications/
rareevent-geoinformatica06.pdf .

projection techniques help users find interesting projections of multidimensional data
sets. The central challenge the geometric projection techniques try to address is how to
visualize a high-dimensional space on a 2-D display.
A scatter plot displays 2-D data points using Cartesian coordinates. A third dimen-
sion can be added using different colors or shapes to represent different data points.
Figure 2.13 shows an example, where X and Y are two spatial attributes and the third
dimension is represented by different shapes. Through this visualization, we can see that
points of types “+” and “×” tend to be colocated.
A 3-D scatter plot uses three axes in a Cartesian coordinate system. If it also uses
color, it can display up to 4-D data points (Figure 2.14).
For data sets with more than four dimensions, scatter plots are usually ineffective.
The scatter-plot matrix technique is a useful extension to the scatter plot. For an n-
dimensional data set, a scatter-plot matrix is an n × n grid of 2-D scatter plots that
provides a visualization of each dimension with every other dimension. Figure 2.15
shows an example, which visualizes the Iris data set. The data set consists of 450 sam-
ples from each of three species of Iris flowers. There are five dimensions in the data set:
length and width of sepal and petal, and species.
The scatter-plot matrix becomes less effective as the dimensionality increases.
Another popular technique, called parallel coordinates, can handle higher dimensional-
ity. To visualize n-dimensional data points, the parallel coordinates technique draws
n equally spaced axes, one for each dimension, parallel to one of the display axes.