Ambient Diagnostics - Ambient Intelligence for Scientific Discovery - page 237

Fig. 7. 3D cluster plot for (Db,a*,b*) for H & P cases.

n -dimensional point becomes a series of ( n − 1) lines connecting the values on

n parallel axes. Berthold and Holve, [52] used this technique to visualize fuzzy
rules underlying 3 classes of irises which resulted from a training set of 75 data
samples with 4 features (petal length, petal width, sepal length, sepal width).
Pham & Brown [54] extended this technique to 3D to provide better visualiza-
tion of the membership function of the fuzzy sets and insight into the strength
of the clustering. We now show how to apply these techniques to analyze the
tongue data.
Since the set of data available at this stage only consisted of 34 tongues (6HP,
5P, 5HC, 2C, 16N), we attempted to cluster this data set through a display in
six parallel coordinates: Db, CI, a*, b*, energy and entropy. Figure 8 shows
the results for three categories: P, H and C. The shaded area representing each
category is obtained by plotting the extent covered by the extreme values for
each coordinate. It can be readily seen that these areas, though overlapped, are
distinguishable from each other.
The order of the coordinates does not change the results, although it might
affect the perceptibility. For example, a large number of intersections might cause
confusion and make it dicult to discern the clusters. Thus, we provided tools
to swap coordinates in order to choose the order with best perceptibility. We
observed that the Cancer cases form a narrow band for all six coordinates as
seen in Fig. 8.
We also observed that for Healthy cases, the variability in feature values is
much greater than in the disease cases. However, this fact can only be confirmed
when more data on disease cases is available. If a much larger set of data is
available, it would also be possible to provide a more sophisticated visualization
by integrating fuzzy sets and using 3D parallel coordinates. We discuss how this
may be achieved in the next subsection.

6.3 Integration of Fuzzy Sets to Visualization

Fuzzy logic has been used extensively and successfully in many areas, especially
in social sciences and engineering. While mathematical models are based on