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2.6 The Dirnensionalitv Ratio Problem 47

05 1
15 05 05 15 2 5 3 5
VAR 1
Figure 2.23. Two class linear discrimination with dimensionality ratio nld = 6.

Figure 2.24. Two class quadratic discrimination with dimensionality ratio nld =lo.

Later on, the data collection task has progressed considerably. We now have
available 30 patterns of each class, distributed as shown in Figure 2.25.
What a disappointment! The classes are largely overlapped. As a matter of fact,
all the data were generated with:

Class 1: Varl = N(l.0, 1); - Var2 = N( I .O, I)
Class 2: Varl = N(1.1, 1); Var2 = N( 1.2, 2)

2
N(m, s) is the normal distribution with mean rn and standard deviation s. In equally scaled
scatter plots, class I is represented by a circular cluster and class 2 by an elliptic cluster
with a vertical axis bigger than the horizo~rtal axis.