## 2 Quality Control Column Set
In both cases, the subjectivity of interpretations is present, and operators' errors are expected, as was recently analyzed by [33] for the case of visual interpreters. Therefore, in order to actually achieve greater accuracy for the RDS, some quality assurance actions need to be deployed in order to reduce the subjectivity of the interpretations. For instance, [34] proposed (i) using a group of selected operators, (ii) designing a specific training procedure for the group of operators in each specific quality control (use case), (iii) calibrating the work of the group of operators in a controlled area, (iv) supplying the group with good written documentation of the product specifications and the quality control process, (v) helping the group with good service support during the quality-control work and socializing the problems and the solutions and, finally, (vi) proceeding to classification based on a multiple assignation process produced by the operators of the group, achieving agreements where needed. The same idea of obtaining more cohesive groups of experts for validation is present in [35], where it is indicated that you have to get a group with common criteria, and, to this end, a five-day workshop should be held. In relation to the achievement of agreement, [36] proposes that validation sampling units be reviewed by nine experts and that the adoption of a label requires a consensus of at least 6 out of 9 among these experts. All of these actions are quality assurance actions and must be deployed, paying special attention to improving trueness (reducing systematic differences between operators and reality), precision (increasing agreement between operators in each case), and uniformity (increasing the stability of operators' classifications under different scenarios). The accuracy of the RDS is of great relevance when considering the statistical tools of thematic quality control. If the RDS does not have the quality to be a reference, the confusion matrix can be understood as a complete multinomial, or an almost complete multinomial if structural zeros are present. From this perspective, the analyses based on the confusion matrix are correct (e.g., overall accuracy, kappa, users' and producers' accuracies, and so on). Thus, if the RDS does have the quality to be a reference, it is not correct to work with the complete confusion matrix because the inherent randomness in the matrix falls down. However, we can manage the data under a new approach that consists of separating the matrix into columns (one for each category) and redefining a multinomial distribution for each category (column). This new idea helps us to clearly differentiate this situation from the previous one based on using the confusion matrix as a complete multinomial. Of course, the thematic quality control data may continue to be displayed as a table (matrix), but the analysis should be carried out by columns. Within this new approach, we propose a method of category-wise control that allows the statement of our preferences of quality, category by category, but also the statement of misclassifications or confusion among classes. These preferences are expressed in terms of the minimum percentages required for well-classified items and the maximum percentage allowed for misclassifications among classes within each column. In order to illustrate the application of the above with an example, Figure 1 shows a confusion matrix from [37] with the results from the accuracy assessment of the classification of a synthetic data set with four categories. Now, let us consider that the RDS used in this assessment does have the quality to be a reference. Therefore, the data from Figure 1 cannot be understood as a complete multinomial but, rather, as a set of four multinomials, one for each category (column). Figure 2 illustrates this fact with locks that symbolize that the marginals of the columns are fixed and therefore, the new structure \"quality control column set\" (QCCS) has to be considered instead of the classical method based on the confusion matrix.