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Davis (1978), and Richards (1986). Separability methods are discussed in Chapter 2. One problem may result from the employment of separability as weighting parameter measure. The assumption underlying each approach is that the data distribution for each class is Gaussian, and consequently that interclass relationships are fully described in the covariance matrices. However, not all data sources are Gaussian in their distribution; for example, the frequency distribution of land elevation measurements is often skewed. In such cases, the use of separability measures may be misleading.

7.5.3 Data-Information class correspondence matrix

Consider that there are a total of I information classes denoted by {α1, α2, …, αI}, and that there are J data classes (e.g. J clusters) denoted by {β1, β2,…, βJ}. The relationship between information classes αi and data classes βj can be represented using conditional probabilities denoted by Pij) that can be used to construct a J by I correspondence matrix M, expressed as:

(7.31)

The objective of the correspondence matrix is to express the strength of the relationship between data classes and information classes. This kind of relationship is sometimes called equivocation. We will give a data source the higher weight if a data class strongly supports the information class. A data source should have lower weight if there is no such strong link between some data classes and information classes. After constructing the correspondence matrix, a meaningful measure is needed to quantify the overall relationships.

In the case in which the linkage between the data classes and the information classes is high, there will be a unique conditional probability in each row of matrix M containing the value of 1, with the remaining entries taking the value 0. Conversely, if a data class is simultaneously linked to several information classes then, in the extreme case, each entry of matrix M will be equal, i.e. there will be no correspondence between the data classes and information classes. A method of expressing these relationships is the entropy measure of Shannon and Weaver (1963). For a particular data class βj, entropy measure E is given by:

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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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