Thematic Accuracy Quality Control by Means of a Set of Multinomials

The error matrix has been adopted as both the “de facto” and the “de jure” standard way to report on the thematic accuracy assessment of any remotely sensed data product. This perspective assumes that the error matrix can be considered as a set of values following a unique multinomial distribution. However, the assumption of the underlying statistical model falls down when true reference data are available for quality control. To overcome this problem, a new method for thematic accuracy quality control is proposed, which uses a multinomial approach for each category and is called QCCS (quality control column set). The main advantage is that it allows us to state a set of quality specifications for each class and to test if they are fulfilled. These requirements can be related to the percentage of correctness in the classification for a particular class but also to the percentage of possible misclassifications or confusions between classes. In order to test whether such specifications are achieved or not, an exact multinomial test is proposed for each category. Furthermore, if a global hypothesis test is desired, the Bonferroni correction is proposed. All these new approaches allow a more flexible way of understanding and testing thematic accuracy quality control compared with the classical methods based on the confusion matrix. For a better understanding, a practical example of an application is included for classification with four categories.