332.

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Page 98

although the ‘wheat’ class shows the highest producer’s accuracy, only 59.3% of the area labelled ‘wheat’ is actually covered by wheat. In other words, 40.7% of pixels classified as wheat are actually other information classes. Thus, the user’s accuracy is really a measure of commission error.

The accuracy measurements shown above, namely, the overall accuracy, producer’s accuracy, and user’s accuracy, though quite simple to use, are based on either the principal diagonal, columns, or rows of confusion matrix only, which does not use the information from the whole confusion matrix. A multivariate index called the kappa coefficient (Cohen, 1960) has found favour. The kappa coefficient uses all of the information in the confusion matrix in order that the chance allocation of labels can be taken into consideration (though Foody (2000a) suggests that chance agreement is overestimated and accuracy is underestimated. He presents an alternative formulation in Foody (1992)).

The kappa coefficient is defined by:

(2.28)

In this equation, is the estimated kappa coefficient, r is the number of columns (and rows) in a confusion matrix, x_ii is entry (i, i) of the confusion matrix, x_i+ and x_+i are the marginal totals of row i and column j, respectively, and N is the total number of observations (Congalton et al., 1983). For computational purposes, the following form is often used:

 

where

 

and

(2.29)

The large-sample variance of kappa is (Congalton and Green, 1998):

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