CROSS-ENTROPY FOR THE EVALUATION OF THE ACCURACY OF A FUZZY LAND-COVER CLASSIFICATION WITH FUZZY GROUND DATA

Fuzzy classifications have been used to represent land cover when pixe ls may have multiple and partial class membership. A fuzzy classificat ion can be derived by softening the output of a conventional ''hard'' classification. Thus, for example, the probabilities of class membersh ip may be derived from a conventional probability-based classification and mapped to represent the land cover of a site. The accuracy of the representation provided by a fuzzy classification is, however, diffic ult to evaluate. Conventional measures of classification accuracy cann ot be used since they are appropriate only for ''hard'' classification s. The accuracy of a classification may, however, be indicated by the way in which the probability of class membership is partitioned betwee n the classes and this may be expressed by entropy measures. Here cros s-entropy is proposed as a means of evaluating the accuracy of a fuzzy classification, by illustrating how closely a fuzzy classification re presents land cover when multiple and partial class membership is a fe ature of both the remotely sensed and ground data sets. Cross-entropy is calculated from the probability distributions of class membership d erived from the remotely sensed and ground data sets. The use of cross -entropy as an indicator of classification accuracy was investigated w ith reference to land cover classifications of two contrasting test si tes. The results show that cross-entropy may be used to indicate the a ccuracy of the representation of land cover when the classification of the remotely sensed data and ground data are both fuzzy.