85.

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Figure 4.14 A hierarchical (three level) partitions from a two-dimension input space.

4.5.2 Experimental results

First, the following non-linear function is used to generate a two-dimensional test image:

(4.42)

where s1 and s2 denote normalised input features (i.e. within the range of [0, 1]). If the input pattern s gives f(s)≥0, then s is placed in class 1, otherwise, s belongs to class 2. Figure 4.15a shows the resulting test (truth) image of size 100×100 in which class 1 is displayed in grey and class 2 is left unshaded. Standard statistical classifiers find difficulty in determining the location of a decision boundary in a problem such as this. Although the class centres for both classes are clearly located, the decision boundary will be a vertical line located at the centre of the horizontal axis.

In order to compare the classification behaviour for different sizes of fuzzy partitions, two fuzzy rule classifiers each with five and twenty partitions on each dimension (i.e. 5²=25 and 20²=400 fuzzy rules in total) were chosen and 400 training samples (selected at random) were used to train the fuzzy rule classifiers. The resulting images classified by both fuzzy rule classifiers are illustrated in Figure 4.15b and c, respectively. It is clear that, in comparison with Figure 4.15b, Figure 4.15c is closer to the original image (Figure 4.15a), but some blockiness can be seen on the boundary.

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