## 5 Results
### Results from the Simulation Dataset
#### 5.2.3 Analysis for Different SNR Conditions  
The fault tolerance to noise is an important index to test the performance of the algorithm. The following discusses the tolerance of the wavelengths selected by the LBI-BPSO, IOIF and GA-BPSO algorithms to noise. As shown in Figure 13, by adjusting the noise term e in Equation (12), the SNRs of the hyperspectral simulation data are gradually reduced from 1280 to 10 for a total of 8 different noise conditions. The values shown in the figure are the average accuracy of 10 repeated runs of the datasets with different SNRs. As described in Section 4.3, in order to compare the performance of different algorithms under the condition of low SNR more intuitively, the change of SNR is in the form of non-uniform step size. Table 4 shows the average and standard deviation of the classification result evaluation at the maximum (SNR = 1280), median (SNR = 160) and minimum (SNR = 10) SNRs, and the optimal value in the table is highlighted. \(\delta\) in this table is the relative numerical difference of the evaluation corresponding to the SNR = 1280 and SNR = 10 conditions. \(\delta\) can be calculated by Equation (15), \(E_{1280}\) and \(E_{10}\) represent the evaluation at SNR = 1280 and SNR = 10, respectively. The smaller the \(\delta\), the smaller the difference in classification performance of the selected wavelength under the two noise conditions of SNR = 1280 and SNR = 10. Furthermore, the algorithm is less affected by noise. Therefore, \(\delta\) can be used to evaluate the noise tolerance of the wavelength selected by the DR algorithm. \[\delta=\frac{E_{1280}-E_{10}}{E_{1280}} \tag{15}\] \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**GA-BPSO**} & \multicolumn{2}{c}{**IOIF**} & \multicolumn{2}{c}{**Partitioned**} & \multicolumn{2}{c}{**LBI-BPSO**} \\ \cline{3-10} \# & **Evaluation** & & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** & **AVG** & **STD** \\ \hline \multirow{3}{*}{SNR = 1280} & OA (\%) & **75.89** & 0.29 & 77.79 & 0.17 & 79.27 & 0.37 & 79.59 & 0.31 \\  & AA (\%) & 75.16 & 0.92 & 75.99 & 0.99 & 78.91 & 1.21 & **79.55** & 0.68 \\  & Kappa (\%) & 66.49 & 0.63 & 68.39 & 0.32 & 71.40 & 0.67 & **71.93** & 0.56 \\  & OA (\%) & 73.45 & 0.16 & 74.44 & 0.34 & 76.44 & 0.95 & **76.75** & 0.14 \\ SNR = 160 & AA (\%) & 71.72 & 1.05 & 72.91 & 1.10 & 74.95 & 1.05 & **75.00** & 0.45 \\  & Kappa (\%) & 62.79 & 0.45 & 62.57 & 0.68 & 67.16 & 1.27 & **67.51** & 0.16 \\  & OA (\%) & 47.99 & 0.51 & 40.36 & 0.37 & 63.59 & 0.58 & **67.78** & 0.23 \\ SNR = 10 & AA (\%) & 39.66 & 1.44 & 32.26 & 0.74 & 57.43 & 0.51 & **62.38** & 0.17 \\  & Kappa (\%) & 23.20 & 1.72 & 12.18 & 0.88 & 47.67 & 0.83 & **53.89** & 0.23 \\ \hline \multirow{3}{*}{\(\delta\) (\%)} & OA & 36.76 & & 48.12 & & 19.78 & & **14.83** \\  & AA & 47.23 & & 57.55 & & 27.22 & & **21.58** \\ \cline{1-1}  & Kappa & 65.18 & & 82.19 & & 33.24 & & **25.08** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Test results of partial SNR conditions. Figure 13: _Cont._From the classification results of the three DR methods shown in Figure 13 and Table 4, it can be found that in terms of the changes in accuracy evaluations with the SNR, LBI-BPSO has always been in a leading position under all standards. Especially in the case of low SNR (SNR \(<\) 80), the selected wavelengths of LBI-BPSO can still obtain relatively good classification results. The decreasing trend of classification accuracy for LBI-BPSO is basically the same as that of Partitioned Relief-F, but LBI-BPSO is more dominant under the condition of low SNR. The classification results of IOIF and GA-BPSO showed a significant decline when SNR \(<\) 80, and were much lower than LBI-BPSO when SNR = 10. The wavelength selected by IOIF is better than GA-BPSO in the case of high SNR (SNR \(>\) 160). In the case of low SNR (SNR \(<\) 80), the IOIF classification results show the fastest decline rate, and the obtained evaluation indicators are all lower than GA-BPSO.