ypical nonlinear classification problem which is called the XOR

A random data set was generated for the XOR problem, which is

Figure 3.24(b). LDA was applied to this data set. Figure 3.24(c)

e density of the projections or predictions (ݕො) of the LDA model.

e seen that two densities of two classes were definitely non-

le. This shows that it was impossible to find a single cutting point

linear classifiers do) to separate two classes of data points using

el. Table 3.6 shows the confusion matrix for applying LDA to this

It can be seen that the classifier gives nothing, but random

(a) (b) (c)

a) The XOR problem. (b) A randomly generated XOR data. (c) Two densities

ses (A and B) of the predictions of a LDA model constructed for this randomly

XOR data.

.6. The confusion matrix of the LDA model constructed for the XOR data.

A

B

%

A

100

100

50.0

B

98

102

51.0

%

50.5

50.4

50.5

ose two LDAs are placed onto this XOR space, which has four

ts labelled by a, b, c, and d, shown in Figure 3.25(a). These two

e labelled by ߙ and ߚ. They are shown as two straight lines in

25(a) because they are linear models. For the LDA ߙ, the data

classified on the left side (assigned a predicted class label as zero)

r three data points are classified on the right side (assigned a