## 3 Results
### Feature Selection Methods  
The UPGMA dendrograms for the twelve \(\sigma^{\circ}\) instances are shown in Figure 4 (_SIG.amp_ and _SIG.amp.FF_) and Figure 5 (_SIG.dB_ and _SIG.dB.FF_); those for \(\beta^{\circ}\) and \(\gamma^{\circ}\) are very similar to those of \(\sigma^{\circ}\) 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: _amp_ and _amp.FF_). 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_ (Figure 5: right). COD also stands out from grouping with the other dispersion variables in \(dB\) and _dB.FF_ (Figure 5: purple), as well as in the original data with no transformation (Figure 4: _amp_ and _amp.FF_). 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_ and _amp.FF_ (Figure 4). This pixel distribution behavior breaks down in \(dB\) and _dB.FF_ (Figure 5: 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 (\(r\sim\)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: purple). A distinctive characteristic is revealed when analyzing \(dB\) (cube and \(\log_{10}\)) and _dB.FF_ (\(\log_{10}\))--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. Table 4 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., \(dB\) and \(dB.FF\) with no transformation and \(\log_{10}\). 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 \(\log_{10}\) (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).