## 3 Results and Discussion
### Phase 5: Attribute Selection Processes
#### 3.5.1 Unweighted Pair Group Method with Arithmetic Mean (UPGMA)  
The combined analysis of dendrograms and correlation matrices show that the 24 COV pair-values have a strong intra-correlation, as well as that they are highly correlated with most of the other variables; hence, they are not further explored. Therefore, out of the 48 initial Oil-Slick Information Descriptors (see Phase 3: Section 2.3.2), only 19 remain for further analyses--Size (6): Area, Per, PtoA, Compact, Fractal, and LEN; and SAR (13): AVG, MED, MOD, MDM, RNG, COD, STD, VAR, AAD, MAD, MAX, SKW, and KUR. However, only half of the NLTs (NLT.0, NLT.5, NLT.6, and NLT.7) utilize these 19 variables; the other half (NLT.1, NLT.2, NLT.3, and NLT.4) explores three fewer Oil-Slick Information Descriptors, i.e., only 16 variables (see Phase 4: Section 3.4). Figure 3 depicts eight UPGMA dendrograms (one for each of the analyzed NLT), in which it is possible to observe a number of differences, as well as resemblances, between them; mostly regarding inter-variable correlations. An evident characteristic of the two Logarithm functions (NLT.2: Log\({}_{10}\); and NLT.3: Ln) is that their dendrograms are equal; the same holds true for their correlation matrices that are also identical. Prior to the uncorrelated variables selection, we have to identify the groups of correlated variables. The process of defining and/or interpreting groups in UPGMA dendrograms is quite subjective [43], but, at first glance, the global picture of Figure 3 clearly reveals how equivalent are the groups between the several NLTs; these are color-coded for clarity. In the visual analysis of Figure 3, one can note that variables tend to group based on their main characteristics, following the Oil-Slick Information Descriptor features, such that:  
* **Green**: Measures of central tendency (AVG, MED, MOD, and MDM);
* **Blue**: Dispersion measures (RNG, COD, STD, VAR, AAD, and MAD);
* **Grey**: Metrics of pixel distribution (SKW and KUR);
* **Yellow**: Basic morphological features (Area and Per) and LEN;
* **Red**: Ratios derived from the morphological features (PtoA, Compact, and Fractal). An advanced analysis of the UPGMA dendrograms shown in Figure 3 discloses that:  
* The three morphological ratios (Red group) are not correlated with any other variable (similarity close to or equal to zero)--PtoA and Compact form an uncorrelated group, and Fractal usually stands alone; the exception is in NLT.0 where Compact is the one by itself;
* The two groups of SAR Information Descriptor, i.e., Green (central tendency) and Blue (dispersion), generally form a larger group--Green + Blue--the exception is in NLT.7;
* The Grey group (pixel distribution metrics) is usually correlated with the Yellow group (basic morphological features)--Grey + Yellow group--the exception is in NLT.7 where it groups with the Green group (measures of central tendency);
* RNG is an exception in three NLTs (NLT.0, NLT.6, and NLT.7) as it correlates with the central tendency variables (Green group);
* MAX groups among the central tendency variables (Green group) except in NLT.4. Figure 3: Rooted tree dendrograms (Unweighted Pair Group Method with Arithmetic Mean: UPGMA—see Phase 5: Sections 2.5.1 and 3.5.1) of the several Non-Linear Transformations (NLTs—see Phase 4: Section 2.4). While the horizontal red dashed line represents the phenon line exploited herein to form groups of variables, i.e., similarity value of 0.3 (i.e., Pearson’s r correlation coefficient), the two horizontal black dotted lines correspond to the more relaxed thresholds reported in our previous investigations [19; 20; 21; 22]. The various color-colored boxes indicate the main groups of variable (see Phase 3: Section 2.3.2). Size Information Descriptors: Yellow [basic morphological oil slick features, i.e., area (Area) and perimeter (Per), and the number of pixels (LEN)] and Red [three ratios derived from the morphological features].