299.

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C is the class variance-covariance matrix of dimension m×m, μ is the class mean vector, and ^T denotes the transpose of a matrix. In some cases, a transformation of D_ij, called the transformed divergence (TD_ij), is used. TD_ij is defined by

(2.7)

in which the value D_ij is projected into interval 0–2000. The greater the value of D_ij or TD_ij, the greater is the class separability based on selected m sub-feature dimension. If expression (2.7) is used, Jensen (1986) points out that generally a poor separability is indicated by a value of TD_ij smaller than 1900 (corresponding to D_ij<23.97).

The B-distance, B_ij, is defined by Haralick and Fu (1983):

(2.8)

The quantity B_ij is computed for every pair of classes given m subfeature dimension. The sum of B_ij for every pair of classes (except the class itself) is obtained and is a measure of the overall separability. Although the two separability measures defined by Equations (2.6) and (2.8) are based on different principles, Mausel et al. (1990) find that the divergence index and B-distance generally give similar results.

2.3 A brief description of pattern recognition techniques

2.3.1 Migrating mean clustering algorithms

The migrating mean clustering algorithm is an example of an unsupervised pattern recognition algorithm. As noted earlier, the main difference between the unsupervised and supervised approaches is that unsupervised methods do not require the user to select training data sets to characterise the targets or to train the classifier. Instead, the user specifies only the number of clusters to be generated, and the classifier automatically constructs the clusters by minimising soe predefined error function. Sometimes, the number of clusters can be detected automatically by the classifier (Gath and Geva, 1989; Krishnapuram et al., 1995). In theory, users do not need to interact with the classifier, which operates independently and automatically. However, in practice, it is more often the case that results are accepted or rejected on the basis of whether or not they meet the user’s expectations.

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