## 3 Results
### Linear Discriminant Analysis (LDA)  
Because our analyses produced many two-by-two tables, we evoke an abridgment of the classic confusion matrix (Table 3) to display the LDA results of the main 39-data instances into a single table, as hierarchized in Table 5. These hierarchies are based on the analyses of the overall accuracy and associated metrics imparted by Table 3. The seep-spill discrimination accuracies of the 22 hybrid schemes (data not shown) fall within the accuracy limits of the main 39-data instances. Therefore, we focus on the information in Table 5, as it conveys the LDA outcomes for all 61-data combinations. These have been obtained after training the algorithms with all 4562 oil slicks. Other metrics can also evaluate the performance of discrimination algorithms (e.g., Cohen's kappa coefficient); however, we choose those in Table 3 as our approach has an operational focus. The discretization interval of our LDAs is 0.02%. This resolution limit represents the smallest detectable difference of the explored dataset--i.e., one misidentified slick: 1/4561. The worst overall accuracy is observed with the original data of the size only combination: 63.90% (2915 slicks correctly identified: 1574 seeps and 1341 spill). The most effective accuracy is observed with the log\({}_{10}\)_GAM.dB_ combination: 68.85% (3141 slicks correctly identified: 1293 seeps and 1848 spill). The first important aspect in Table 5 is that key hierarchy-accuracy groupings are formed. There are three major blocks influenced by the data transformations. Some combinations are deemed to perform better than others--top-down: log\({}_{10}\), cube root, and no transformation. Within these major blocks, the SAR calibrated products are grouped forming minor blocks; usually _dB_ (with or without _FF_) summits most effectively (except in cube root, where _amp.FF_ reaches better accuracy). The SAR backscatter coefficients are distributed within these minor blocks, where \(\gamma^{\circ}\) tends to have better accuracies. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Hierarchy** & **Data Transformation** & **Oil-Slicks’** & **Signature** & **Oil Seeps** & **Oil Spills** & **Oil Slicks** \\ \hline
1 & log\({}_{10}\) & Gamma-naught & _dB_ & 1293 & 64.84\% & 1848 & 71.96\% & 3141 & 68.85\% \\  & & & & 64.23\% & & 72.50\% & & \\ \hline
2 & log\({}_{10}\) & Beta-naught & _dB_ & 1292 & 64.79\% & 1848 & 71.96\% & 3140 & 68.83\% \\  & & & 64.21\% & & 72.47\% & & & \\ \hline
3 & log\({}_{10}\) & Sigma-naught & _dB_ & 1292 & 64.79\% & 1845 & 71.85\% & 3137 & 68.76\% \\  & & & 64.12\% & & 72.44\% & & & \\ \hline
4 & log\({}_{10}\) & Gamma-naught & _dB.FF_ & 1293 & 64.84\% & 1842 & 71.73\% & 3135 & 68.72\% \\  & & & 64.04\% & & 72.43\% & & & \\ \hline
5 & log\({}_{10}\) & Sigma-naught & _dB.FF_ & 1292 & 64.79\% & 1838 & 71.57\% & 3130 & 68.61\% \\  & & & 63.90\% & & 72.36\% & & & \\ \hline
6 & **log\({}_{10}\)** & **Size only** & **1288** & **64.59\%** & **1841** & **71.69\%** & **3129** & **68.59\%** \\  & & & **63.92\%** & & **72.28\%** & & & \\ \hline
7 & log\({}_{10}\) & Beta-naught & _dB.FF_ & 1288 & 64.59\% & 1840 & 71.65\% & 3128 & 68.57\% \\  & & & 63.89\% & & 72.27\% & & & \\ \hline
8 & log\({}_{10}\) & Sigma-naught & _amp.FF_ & 1321 & 66.25\% & 1806 & 70.33\% & 3127 & 68.54\% \\  & & & 63.42\% & & 72.85\% & & & \\ \hline
9 & log\({}_{10}\) & Sigma-naught & _amp_ & 1323 & 66.35\% & 1803 & 70.21\% & 3126 & 68.52\% \\  & & & 63.36\% & & 72.88\% & & & \\ \hline
10 & log\({}_{10}\) & Beta-naught & _amp_ & 1324 & 66.40\% & & & \\ \hline
11 & log\({}_{10}\) & Gamma-naught & _amp_ & 1320 & 66.20\% & & & \\ \hline
12 & log\({}_{10}\) & Gamma-naught & _amp_ & 1320 & 66.20\% & & & \\ \hline
13 & log\({}_{10}\) & Beta-naught & _amp_ & 1320 & 66.20\% & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Outcomes of our linear discriminant analyses (LDAs). Refer to Table 3 for explanations.