## 2 Materials and Methods
### Exploratory Data Analysis  
Even though our current research follows an equivalent pattern as before (see Section 2.3), we take advantage of our previously acquired understanding [29; 30; 31; 32; 33; 34] to reorganize the blueprint of our exploratory data analysis (Figure 2) into a more rigorous detail-oriented scheme:  
* **SAR Signature:** To verify which combination of SAR backscatter coefficients with SAR calibrated products provides the finest discrimination accuracy, we separately perform a complete analysis exploring the full SAR signature set (12)--i.e., _SIG.amp_, _SIG.amp_.FF_, _SIG.dB_, _SIG.dB_.FF_, _BET.amp_, _BET.amp_.FF_, _BET.dB_, _BET.dB_.FF_, _GAM.amp_, _GAM.amp_.FF_, _GAM.dB_, and _GAM.dB_.FF_; respectively for \(\sigma^{\circ}\), \(\beta^{\circ}\), and \(\gamma^{\circ}\), given in _amp_ and in _dB_, with or without a despeckle filter (FF; for Frost filter [62]). This differs from the initial exploratory analysis that analyzed all calibrated products together for each backscatter coefficient [29; 30]. * **Explored Attributes:** We apply the minimum value-scaling filter, and because we also intend to reduce dimensionality, histograms and correlation matrices are examined in an attempt to reduce the number of variables included in our analyses. * **Data Transformations:** To evaluate the impact of the two best non-linear transformations found in the first refined study (i.e., cube root and log\({}_{10}\)) we compare them with the original data with no transformation. * **Feature Selection Methods:** We also avoid PCAs and solely use dendrogram analyses with the strict phenon threshold (\(r=0.3\)), as indicated by the results of the first refined study [31; 32]. * **Linear Discriminant Analysis (LDA):** Our LDA-based algorithms involve an analysis of a number of combinations of the three backscatter coefficients, each of which is calculated from the four calibrated products and the three data transformations (36 instances). We also investigate the standalone use of the size information with the tested transformations (3 instances); these are referred to as size only. We also consider 22 extra combinations using several of the main 39-data instances analyzed together--\"hybrid schemes\"--resembling those used by [75; 76]. Therefore, \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{Diagonal} & **A** & **=** & **Correctly identified oil seeps** \\  & **D** & **=** & **Correctly identified oil spills** \\ \cline{2-4}  & **A + D** & **=** & **Correctly identified oil slicks** \\ \hline \multirow{3}{*}{Off-Diagonal} & C & = & Misidentified oil seeps \\  & B & = & Misidentified oil spills \\ \cline{2-4}  & C + B & = & Misidentified oil slicks \\ \hline \multirow{3}{*}{Horizontal Analysis of Table 1} & A + B + C + D & = & Known oil selects (i.e., 4562) \\  & A + B & = & Known oil seeps (i.e., 1994) \\  & C + D & = & Known oil spills (i.e., 2568) \\ \cline{2-4}  & **A/(A + B)** & **=** & **Sensitivity** \\  & **D/(C + D)** & **=** & **Specificity** \\ \cline{2-4}  & B/(A + B) & = & False negative \\  & C/(C + D) & = & False positive \\ \hline \multirow{3}{*}{Vertical Analysis of Table 1} & A + C & = & LDA classified oil seeps \\  & B + D & = & LDA classified oil spills \\ \cline{2-4}  & **A/(A + C)** & **=** & **Positive predictive value** \\  & **D/(B + D)** & **=** & **Negative predictive value** \\ \cline{2-4}  & C/(A + C) & = & Inverse of the positive predictive value \\  & B/(B + D) & = & Inverse of the negative predictive value \\ \hline \hline \multicolumn{4}{c}{**(A + D)/(A + B + C + D)**} & **=** & **Overall accuracy** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: List of statistical standard metrics associated with the confusion matrix [75; 76; 77]. See Table 1 for A, B, C, and D. Bold indicates relevant metrics explored herein—refer to Table 3.  
we investigate 61-dataset combinations.