3.1. Explored Attributes
We removed certain attributes at the start of our analyses using three major correlation matrices: one for each data transformation, accounting for the three backscatter coefficients and four calibrated products, accounting for the 19 variables from the first refined study [31
]. Accordingly, herein, we simply explore the information of 13 variables, thus reducing the dimensionality of the problem in relation to our earlier investigations (Figure 3
). This set of variables are collectively referred to as the oil-slicks’ signature:
Ratio between Per and Area (PtoA [78
Compact index (4.π.Area/Per2
Fractal index (2.ln(Per/4)/ln(Area) [79
Standard deviation (STD);
Coefficient of dispersion (COD: the third interquartile minus the first, divided by their sum);
Skewness (SKW); and
The first five correspond to the size information and the next eight are the SAR basic qualitative-quantitative statistics. The latter are divided in: central tendencies (AVG, MED, and MOD), measures of dispersion (STD, VAR, and COD), and pixel distribution metrics (SKW and KUR).
An imperative information is that when log10 is applied, only 10 variables are accounted, as Fractal, SKW, and KUR have negative values preventing their use.
3.2. Feature Selection Methods
The UPGMA dendrograms for the twelve σ° instances are shown in Figure 4
) and Figure 5
); those for β° and γ° are very similar to those of σ° independent of data transformation. Using the strict threshold (dotted horizontal phenon similarity line: r
= 0.3), we select one variable (+) from each resulting group. Groups of similar (correlated) variables are color-coded to facilitate visual interpretation.
The central tendency (green) and dispersion (blue) variables group between each other, and together they form a single group (Figure 4
). The behavior of the central tendency and dispersion counterparts is disturbed when variables are dB
transformed (purple), such that KUR becomes part of this group once no transformation or cube root occur (Figure 5
: left); though, this is not observed in dB.FF
: right). COD also stands out from grouping with the other dispersion variables in dB
: purple), as well as in the original data with no transformation (Figure 4
). From this larger green-blue group VAR is selected.
The pixel distribution (gray) pairs with the twosome of Area and Per (yellow) while in amp
). This pixel distribution behavior breaks down in dB
: left and right). From this gray-yellow larger group KUR is selected.
The size information ratios (red) do not show correlation with any other attribute (r
~0.0). As such, they are selected when present—i.e., no transformation and cube root. They tend to assemble (Figure 4
), but sometimes this do not hold true (Figure 5
A distinctive characteristic is revealed when analyzing dB
(cube and log10
) and dB.FF
)—see (*) in Figure 5
. All variables possess significant statistical correlation—i.e., their relationships exceed below the phenon similarity strict threshold of r
= −0.3. Although no variable should have been selected, to avoid such disrupting action we selected comparable attributes with the other analyses to perform a second round of dendrogram analysis only with these variables (+). Indeed, their selection shows no intra-correlation—this is also supported by the major correlation matrices.
lists the UPGMA uncorrelated variables selected for each of the main 39–data instances. Most combinations (26) include the three size information ratios: PtoA, Compact, and Fractal – only in the log-transformed ones (13) whereby Fractal is not present as it accounts for negative values. Some combinations (12) also have Area selected, i.e., dB
with no transformation and log10
. Of the 36–data instances exploring SAR basic statistics, VAR is selected in all of them. In almost all (18) not- and cube-transformed combinations, KUR is chosen, and in only three instances SKW is selected in its place: dB
with no transformation. Thus, usually (in 15 instances), we have five attributes as the most frequently used in the LDA-based algorithms: PtoA, Compact, Fractal, VAR, and KUR; independent of SAR backscatter coefficient, SAR calibrated product, or data transformation. The number of selected attributes varies from two to six (Table 4
Two variables are selected in only one instance: size only log-transformed (1).
Three attributes are chosen in eight instances: size only with no transformation and log10 (2), and dB and dB.FF log-transformed (6).
Four variables are selected in nine instances: cube-dB (3), and amp and amp.FF log-transformed (6).
Five attributes are accounted in the largest set of instances (fifteen): amp and amp.FF with no transformation (6), and all cube-transformed ones (9) not including dB.
Six variables are selected in six instances: when no transformation is applied to dB and dB.FF (6).
Comparing our SIG.amp
dendrograms (Figure 4
: left panels) with those from the refined study [31
], the removal of six attributes to start the analysis (13 against 19) causes only a minor impact on the similarity of the retained variables, and yields small changes in the in-group configuration using the same strict similarity cut-off (r
= 0.3). The main exception occurs in the log-transformation Figure 4
(bottom left), in which the size information similarities are altered, but not influencing the grouping of the variables, nor the selected features. The selection of uncorrelated attributes only varies between this research and prior approach [31
] because we opt to select different variables within the formed groups (i.e., VAR instead of AVG, and KUR in lieu of SKW).
3.3. 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 log10 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: log10
, 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 γ° tends to have better accuracies.
Quantifying the hierarchy misidentification of the data transformation blocks (Table 5
), we observe that the log10
combinations have the best overall accuracy (GAM.dB
: 68.85%). The log10
combinations have the best oil-spill identification rate (1848 GAM.dB
) but correctly detect the least amount of oil seeps (1288: BET.dB.FF
). On the other hand, the not-transformed original data are inversely propositional to log10
—i.e., have a poorer overall accuracy (size only: 63.90%) being the worst one to identify oil spills (1341: size only) but the best one to correctly identify oil seeps (1580: GAM
, both with amp
presents a summary of the seep–spill discrimination statistics regarding the transformation blocks. Even though the log-transformed combinations (GAM.dB
: 68.85%) outperform the cube-combinations (GAM.amp.FF
: 68.35%), the latter show more balanced seep–spill correct identification capabilities. The unbalanced seep (spill) log10
dispersal is: min 1288 (1799) and max 1324 (1848). The balanced min seep (spill) correct cube root identification is 1378 (1685) and its max seep (spill) correct detection is 1410 (1730). Equivalently, the best original not-transformed data also have a fairly balanced seep (spill) identification rate; however, with less oil slicks correctly identified (GAM.dB.FF
: 65.67%)—min 1554 (1341) and max 1580 (1433).
From Table 6
we also note the range (226) of the three transformations: oil slicks correctly identified varied from 3141 (log10 GAM.dB
) to as low as 2915 (not-transformed size only). While the oil seeps’ range (292) varied from 1580 (no transformation: GAM
, both with amp
) to 1288 (log10 BET.dB.FF
), the oil spills’ range is larger (507) and goes from 1848 (log10 GAM.dB
) to 1341 (not-transformed size only). Some equivalence exists between the seep, spill, and slick ranges of the log10
(36, 49, and 22) and cube (32, 45, and 33) combinations. The original data ranges are: 26 (seeps), 92 (spills), and 81 (slicks).
also shows that, on average, the overall accuracy of all oil slicks is 67.13%. If considering the average of the log10
(68.60%) and cube (68.12%) combinations, these have similar discrimination performances, though, as pointed out, the latter surpass the former with its more balanced seep–spill discrimination. The original data with no transformation had the lowest discrimination overall accuracy average: 64.68%.
The second remarkable aspect observed in Table 5
is related to the hierarchy-accuracy grouping of the original not-transformed data. None of its 13 data instances are valid. They had very low (<60%) specificity (i.e., of the a priori know spills, how many the LDA identifies correctly?) and positive predictive values (i.e., of the LDA-identified seeps, how many are actually seeps?). This means that the data needs to be normalized to achieve success in discriminating the oil-slick category using our linear approach.
The third noteworthy aspect observed in Table 5
concerns the choice of variables, i.e., oil-slicks’ signature: size information and SAR basic qualitative-quantitative statistics—see (@) in Table 4
. To this matter, we call a comparison between our current research (Table 5
) and the first refined study (Table 7
). Even though the SAR basic statistics we select now (SIG.amp
: VAR and KUR) are different from the ones of the refined study (SIG.amp
: AVG and SKW), there is not much change in the discrimination power between the two analyses. This is independent of the way the data is transformed, for instance, SIG.amp
(68.52% against 68.50%), cube (68.08% against 68.35%), and no transformation (64.25% against 63.88%), respectively, for our current research and the first refined study [31
The same holds true when we verify the size only combinations (see (@) in Table 4
) between now (Table 5
) and then (Table 7
). In our current research we account for three size information variables (Table 4
: PtoA, Compact, and Fractal), whereas in the refined study only two were used (Table 7
: PtoA and Compact). Again, these discrimination outcomes are quite close, with size only log10
categorizing exactly the same oil slicks in our current research (Table 5
) and in the refined study (Table 7
(68.59% against 68.59%), cube (67.62% against 67.60%), and no transformation (63.90% against 63.85%), respectively, for our current research and the first refined study [31
We also note in Table 7
that the analyses of the size and SAR signatures together (i.e., SIG.amp
) do not impact the outcomes much. For the log-transformed discrimination accuracy, in fact, it worsens the overall accuracy: 68.59% (size only) and 68.50% (size and SAR together). However, it does impact the cube-transformed, improving its seep–spill categorization capacity: 67.60% and 68.35%, respectively. For the original not-transformed data, only one oil slick is differently classified. Similar patterns happen in our current analysis (Table 5
The accuracy behavior of the oil-slicks’ signature (size and SAR), on the other hand, is actually slightly different once we account for the other SAR backscatter coefficients and SAR calibrated products (Table 5
). In the relation to the data transformations, size only has the poorer performance of all instances in both no transformation (63.90%) and cube root (67.62%), but when the SAR signature is taken into account we obtain improved accuracies: no transformation (GAM.dB.FF
: 65.67%) and cube root (GAM.amp.FF
: 68.35%). Likewise, when we compare the log10
instances size information without (size only: 68.59%) and with the SAR signature (GAM.dB
: 65.85%), there is also an improvement; smaller though.