84.

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Page 173

i.e. wij=1. However, if the value βx, for all class x, are close to each other, i.e. β1≈β2≈…≈β1, then the rule will fire at its lowest strength, i.e. wij ≈0. The determination of rule strength may be achieved in other ways. One possible choice for specifying the rule strength can be in terms of an entropy measure, and the strength wij may be defined as:

(4.41)

Highly entropy indicates that the values of all βx are all relatively similar, hence rule strength should be decreased, while low entropy indicates that rule strength should be larger. It is likely that rule strength will vary with different measuring methods, and will therefore affect classification accuracy. One may test different approaches for determining rule strength, and compare the classification results.

Since the approach described above for generating fuzzy rules from the training data, the effect of the size of fuzzy subspace should be considered. If the fuzzy subspace is too small, there will be a high probability that some fuzzy subspaces (called dummy subspaces) may contain no training data and therefore cannot generate any fuzzy rules. In such a situation, the image pixels falling within these dummy subspaces cannot be classified. On the other hand, if the fuzzy subspace is too large, some fuzzy subspaces may contain a variety of different classes of data, and this will decrease the classification power of fuzzy rule classifier.

Ishibuchi et al. (1992) suggested a hierarchical strategy for solving this space-partitioning problem. Their method is quite straightforward, and involves the partitioning of the input feature space into different sizes of fuzzy subspaces, from large to small, as a hierarchical structure shown in Figure 4.14. The inference engine then simultaneously employs all rules for determining αx and αc in Figure 4.13b. Although this method can improve classification performance, the resulting computation time will increase substantially, and so will the rule storage requirements. For example, if the maximum number of fuzzy partitions for each input dimension is determined as 20, the total number of rules will be 22+32+…+202. Such a large number of rules will generate a considerable computation burden. Another solution to the fuzzy subspace partition problem is based on the density of the training data. Large fuzzy partitions are suitable for areas of feature space that have a low density of training data, whilst for areas containing a high density of training patterns the smaller partition of fuzzy subspaces should be applied (Abe and Lan, 1995).

[Cover] [Contents] [Index]


Classification Methods for Remotely Sensed Data
Classification Methods for Remotely Sensed Data, Second Edition
ISBN: 1420090720
EAN: 2147483647
Year: 2001
Pages: 354

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