## 3 Results and Discussion
### Phase 8: Confusion Matrices (2-by-2 Tables)  
Each NLT is evaluated with the four input dataset versions (Figure 4), and usually, Set.1 presents the highest discrimination power. However, these variables (16 or 19) are strongly correlated (Figure 3) and do not fulfill a Discriminant Functions requirement to use independent, or the least as correlated as possible, attributes [62]. The second best discrimination accuracy occurs with Set.2, which is closely followed by Set.3. The lowest observed accuracies are from Set.4, as the selected PCs have a very low cumulative variance in the selected PCs; the exceptions are the Logarithm functions (NLT.2: Log\({}_{10}\); and NLT.3: Ln--see Table 4). The global analysis of all 32 Data Transformation Approaches combinations (i.e., eight NLTs versus four input dataset versions) demonstrates the Logarithm functions (NLT.2: Log\({}_{10}\); and NLT.3: Ln) and Cube Root (NLT.6) as the most effective NLTs in supporting an accurate Oil-Slick Discrimination Algorithm. The Confusion Matrices evaluating the results of the Discriminant Functions for the several NLTs are shown on the color-coded Table 5 (Pink) and Table 6 (Red): Set.2 and Set.3, respectively. In the examination of these two tables that report the accuracy of the Oil-Slick Discrimination Algorithm, if taking the Log\({}_{10}\) (NLT.2), for example, one can find that:  
* **CM.1**: Overall Accuracies ranging about 69%;
* **CM.2**: Producer's Accuracy, i.e., Sensitivities (65%) or Specificities (71%);
* **CM.2**: Commission Error, i.e., False Negative (35%) and False Positive (29%);
* **CM.3**: User's Accuracy, i.e., Positive (64%) and Negative (73%) Predictive Values;
* **CM.3**: Omission Error, i.e., Inverse of the Positive (36%) and Negative (27%) Predictive Values. From Tables 5 and 6, one verifies the successful, and similar, results of the Cube Root (NLT.6) in comparison to the Logarithm functions (NLT.2 and NLT.3). Additionally, the cross-comparison of the results from Set.2 (Table 5) and Set.3 (Table 6) indicates that these two attribute selection strategies--i.e., 1) no UPGMA variable selection with PCA; and 2) UPGMA selected variables without PCA--promote comparable seep-spill discrimination accuracies. Figure 4: Discriminant Functions explored to discriminate oil seeps from oil spills: (**a**) All variables; (**b**) Separate analysis of Size Information Descriptors (Area with Perimeter and PtoA with Compact); and c) Separate analysis of SAR Information Descriptors (AVG with SKW). The four input dataset versions are shown: all variables (16 or 19—see Phase 5: Section 3.5.1; Figure 3 and Table 3) without (Set.1) and with (Set.2) PCA (Principal Component Analysis—see Phase 6), UPGMA (Unweighted Pair Group Method with Arithmetic Mean—see Phase 5: Section 2.5.1) attribute selection (i.e., 4 to 7 variables—see Phase 5: Section 3.5.1; Figure 3 and Table 3) without (Set.3) and with (Set.4) PCA. 8\(\times\) refers to the several Non-Linear Transformations (NLT—see Phase 4: Section 2.4); 3x to the best NLT: NLT.0, NLT.2, and NLT.6; and 2\(\times\) to NLT.0 and NLT.6. * See Figure 3. ** See [19; 20; 21; 22]. A careful analysis of Table 5 (Set.2) discloses that the preferred lowest rate of False Negatives (20.4%) and Inverse of the Positive Predictive Values (23.3%) are observed in NLT.1 (Reciprocal); however, their counterparts, i.e., False Positives (48.0%) and Inverse of the Negative Predictive Values (43.7%), have undesirable high values among all NLTs. As its Overall Accuracy is reasonable (64.07%), this is an example that one needs to look into the conjunct interpretation of the five main metrics shown in Table 1[19; 20; 21; 22; 63; 64; 65]. Similarly, the cautious analysis of Table 6 (Set.3) reveals that an ideal low rate of False Negatives (11.7%) and Inverse of the Positive Predictive Values (21.8%) are observed in NLT.5 (Square Power), but on the other hand, their counterparts, i.e., False Positives (67.5%) and Inverse of the Negative Predictive Values (49.6%), have unwanted high values.