## 2 Quality Control Column Set  
In this section, we first present an approximation to what a confusion matrix is and, subsequently, we present the concept of QCCS and the difference between the two approaches. The aspect that differentiates both approaches--the quality of the reference data--is highlighted. A confusion matrix, or error matrix, is a contingency table, which is a statistical tool for the analysis of paired observations. The confusion matrix is proposed and defined as a standard quality measure for spatial data (measure #62) by ISO 19157 [6] in Annex D with the name \"misclassification matrix\" or \"error matrix\". For a given geographical space, the content of a confusion matrix is a set of values accounting for the degree of similarity between paired observations of k classes in a controlled data set (CDS), and the same \(k\) classes of a reference data set (RDS):  
\[\text{CM(i,j)}=[\text{\#items of class (j) of the RDS classified as class (i) in the CDS}]. \tag{1}\]  
As indicated by the study presented in [19], the most frequent number of classes \(k\) is between 3 and 7, although there are matrices that reach up to 40 categories. Usually, the RDS and CDS are located by columns and by rows, respectively. So, it is a \(k\times k\) squared matrix. The diagonal elements of a confusion matrix contain the number of correctly classified items in each class or category, and the off-diagonal elements contain the number of confusions. So, a confusion matrix is a type of similarity assessment mechanism used for thematic accuracy assessments. A confusion matrix is not free of errors ([17,20]), and for this reason, a quality assurance of intervening processes is needed, e.g., the proposal of [11] can be considered in this way (in order to apply a statistically rigorous accuracy assessment). As pointed out by [21], obtaining a reliable confusion matrix is a weak link in the accuracy assessment chain. Here, a key element is the RDS, denoted sometimes as the \"ground truth\", which can be totally inappropriate and, in some cases, very misleading [10] and should be avoided ([22,23]). As pointed out by several studies ([24,25,26,27]), the RDS often contains errors and sometimes possibly more errors than the CDS. Here, the major problem comes from the fact that classifications are often based on highly subjective interpretations [28]. The problem with a lack of quality in the reference data is still current [29], and the thematic quality of products derived from remote sensing still presents problems [30]. We understand that this situation is due to the fact that, in most cases, the RDS is simply another set of data (just another classification) and not a true reference (error-free or of better quality). The above-mentioned situation does not occur in the quality assessment of other components of spatial data quality; in this way, as indicated by [31], compared to positional accuracy, there is a clear lack of standardization. For example, in the case of positional accuracy, the ASPRS standard [32] establishes the following requirement: \"The independent source of higher accuracy for checkpoints shall be at least three times more accurate than the required accuracy of the geospatial data set being tested\". This situation is directly achievable when working with topographic and geodetic instruments, but it is not directly attainable when working with thematic categories because of the high subjectivity of interpretations ([28; 33]). However, we believe that this situation should guide all processes for determining the RDS of an assessment of thematic accuracy. In this sense, as an example of good practices in accuracy assessment, [8] the higher quality of the sample is included as a fundamental premise. RDSs are usually derived from ground observations or from image interpretations. Fieldwork derived from ground observation is the most accurate possible source for thematic accuracy assessment, but it may be cost-prohibitive for many projects. For this reason, common image interpretations are preferred.