# Single-Class Data Descriptors for Mapping
## 2 Materials and Methods
### Performance Evaluation  
In this study, the error computation and performance evaluation involve several accuracy metrics, i.e., the basic errors (see Table 2), \(F_{1}\) measure, receiver operating characteristics (ROC) curve, area under the ROC curve (AUC) error, cost curve, confusion matrix, and correct rate, which are employed to evaluate the SCDDs in a more comprehensive way. In order to find a good SCDD, four basic errors can be calculated, and two of them have to be minimized, namely the false positives (FP) and false negatives (FN). Hence, we put forward and discuss several representative measures which can reflect the probability that the prediction is informed versus chance. The FN can be estimated on the positive set. In fact, the FN is much harder to estimate when no negative samples are available [47]. If onlyminimizing the FN will lead to the SCDD which may wrongly label a number of the negative samples as the positive class. In order to avoid such a degenerate solution, the negative samples have to be collected as well. This is the reason why we elaborately prepared the design sets and the reference results for training and testing. Moreover, two other measures, such as precision and recall (i.e., the true positive (TP) rate), are often used in performance evaluation. Finally, a derived performance indicator \(F_{1}\) score can be computed. Note that a good SCDD should have both small rates of the FN and FP.  
Due to the error on the positive class can be estimated relatively well, assuming that, a threshold can be set beforehand on the target error for the SCDDs, and then a ROC curve can be obtained by varying this threshold and measuring the error on the negative samples. The ROC graph [69; 70] shows how the FP varies for varying the FN, which is a technique for visualizing and selecting the best classifiers based on their performance. The smaller these fractions are, the more the SCDD is to be preferred. Although the ROC graph shows an intuitive metric of the performance of the SCDD, as one side, it is a bit difficult to compare the ROC curves; for another, we want to reduce the ROC curve to a single scalar value representing the expected performance. Thus, the AUC error [71; 72] often is taken, and which is computed from the ROC curve, which integrates the fraction TP over varying thresholds (or by varying fraction FP equivalently). The larger the AUC value, the better the SCDD's performance. That is, the higher values may indicate a better separation between the positive and negative samples. As for the ROC graph [70], there are many thresholds that may be suboptimal. That is, there is another operating point for which at least one of the errors is lower. Nevertheless, this concern can be indicated by a cost curve [73], which will be another method for visualizing the performance of the SCDD. For a varying cost-ratio between both classes, the expected cost is computed. Additionally, once a trained mapping has been determined, we can obtain the sufficient site-specific metrics derived from a confusion matrix (i.e., a binary contingency table for the SCDD). The binary confusion matrix (see Table 2) is a specific table layout that allows the visualization of the performance of the SCDD [74]. Such an error matrix is constructed via classifying a predefined test set or comparing two sets of labels, and which combines the spatial position and quantitative information of the classification results to implement a performance evaluation. What is important is that the very small changes of labels are well reflected in a confusion matrix.