## 5 Results
### Results from the Simulation Dataset
#### 5.2.2 Analysis for Different Abundances  
In order to further discuss the influence of different abundances of mixed pixels on the classification accuracy, Figure 12 shows the correspondence between the classification accuracy of ground objects and the abundance of mixed pixels when the SNR is 1000. In the range of abundance from 0.55 to 0.75, the classification evaluation of mixed pixels according to the PA definition is AVA (Abundance Variable Accuracy) and total average TA. AVA is a variable defined in this paper for the convenience of description. It is obtained from the average value of \(N\) Product's accuracy PA calculated from mixed pixels of a certain ground object and other \(N\) objects under the specified abundance.  
The AVA corresponding to a mixed pixel of the ground object \(i\) with abundance \(x\) (\(x>0.5\)) is described by Equation (13), where \(n\) is the number of other objects categories except feature \(i\), and PA\({}_{ij}^{x}\) is the Product's accuracy of the mixed pixel with object \(j\) when the abundance of object \(i\) is \(x\). Correspondingly, the total average value TA is the average value of AVA\({}_{i}^{x}(x=1,2,\ldots,N_{a})\) for the ground object \(i\) at different abundances \(x\) and calculated by Equation (14). \(N_{a}\) is the number of abundance variables. According to the settings of mixed pixel abundance and single-label classification strategy in Section 4.3, \(N_{a}\) is 5 in this paper, as shown by the abscissa in Figure 12.  
Figure 11: (**a**) Simulation data label diagram (Ground Truth); (**b**) original wavelength; (**c**) GA-BPSO; (**d**) IOIF; (**e**) Partitioned Relief-F (**f**) LBI-BPSO.  
\[\text{AVA}_{i}^{x}=\frac{\sum\limits_{j=1}^{N}\text{PA}_{ij}^{x}}{N} \tag{13}\]  
\[\text{TA}_{i}=\frac{\sum\limits_{x=1}^{N}\text{AVA}_{i}^{x}}{N_{a}} \tag{14}\]  
Figure 12 shows the performance of the three DR algorithms on AVA and TA for vegetation, green coating, artificial leaves, and camouflage cloth. It can be found that the wavelength results of LBI-BPSO for vegetation, artificial leaf and camouflage cloth have better performance at most abundances, and its TA values are greatly improved compared to IOIF and GA-BPSO. It can be seen that the advantage of LBI-BPSO in distinguishing the green-coating mixed pixels is not significant, but the TA is still at the highest level. Overall, the wavelength selection results of LBI-BPSO showed better classification performance compared to IOIF and GA-BPSO at different abundances.  
At the same time, the performance of LBI-BPSO and Partitioned Relief-F are relatively close in both AVA and TA. Interestingly, looking at Figure 12, it can be found that the accuracy is not positively correlated with the increase in the abundance of target objects. This is due to the similar color and material variability of the samples selected in this paper, and the partial spectra of various ground objects are close. There is, in addition, some high-abundance data obtained by mixing the spectra of the two types of ground objects by Equation (12) just show a higher similarity with the spectrum of the third type of ground objects, resulting in misclassification when the abundance is high. For example, Figure 12 shows that the green coating and artificial leaf did not increase AVA at an abundance of 0.75. Combined with the classification results in Figure 11c-e, it can be found that in the mixed areas M23 and M32 of green coating and artificial leaf, there are a large number of pixels in the area close to pure pixels that are classified as vegetation, resulting in a large number of classification noise.  
Figure 12: Cont.  
Figure 12: Evaluation of classification results under different abundances (SNR = 1000). (**a**) Vegetation; (**b**) Green coating; (**c**) Artificial leaves; (**d**) Camouflage cloth.