# Quadratic Clustering-Based Simplex Volume Maximization for Hyperspectral Endmember Extraction
## 3 Results and Discussion
### Results for Endmember Extraction  
In this part, the performance of all algorithms on endmember extraction is compared. According to the previous parameter analysis, s, \(\lambda_{1}\), Pt, \(\lambda_{2}\) and k are set to 6, 0.1, 0.4, 0.4 and 5*p respectively. Figures 11-13 give the comparison between the estimated and ground-truth endmember spectral signatures of Samson, Jasper Ridge and Cuprite, respectively. The SAD calculation results are shown in Table 1.  
Figure 11: Comparison between the estimated and ground-truth endmember spectral signatures on Samson. (**a**) Soil; (**b**) tree; (**c**) water.  
To clearly show the comparison, the results of several test algorithms that perform better are drawn in the figures above, including VCA, AVMAX, SENMAV, SPEW and ECSO. From Figure 11, most algorithms can accurately extract soil and tree, but have a relatively large extraction error on water. CSVM achieves the best extraction accuracy on soil and water, as the curves almost coincide with the ground truth. Figure 12 shows the comparison for Jasper Ridge. According to the curves, all endmembers obtained by CSVM show the best consistency with ground truth in terms of shape and reflectance value. Figure 13 depicts the results for Cuprite. It is difficult to directly evaluate the algorithms through the curves since they all have difference with the ground truth in both shape and reflectance value. Therefore, quantitative analysis is necessary for further evaluation.  
Table 1 shows the results of SAD. In Samson, CSVM obtains the best SAD for Soil and Water. SGA fails to extract water, as it gets a SAD more than 1, and KMEE fails to extract tree. CSVM provides best SADs on all endmembers in Jasper Ridge. SGA and KMEE are unable to extract water, and AMEE fails to extract road. All algorithms extract endmembers in Cuprite. CSVM gets the best results on tumorigenic and chalcedony. CSVM does not achieve best extraction accuracy on all endmembers. For those that do not get the best SAD, such as tree in Samson, muscovite in Cuprite and so on, CSVM obtains the results that are very close to the best values. Overall, CSVM provides the best averages for all datasets, corresponding to 0.0179, 0.0599 and 0.0873, respectively.  
Figure 12: Comparison between the estimated and ground-truth endmember spectral signatures on Jasper Ridge. (**a**) Tree; (**b**) water; (**c**) soil; (**d**) road.  
Figure 13: Comparison between the estimated and ground-truth endmember spectral signatures on Cuprite. (**a**) Alunite; (**b**) andradite; (**c**) buddingtonite; (**d**) tumorigenite; (**e**) kaolinite1; (**f**) kaolinite2; (**g**) muscovite; (**h**) montmorillonite; (**i**) nontronite; (**j**) pyrope; (**k**) spine; (**l**) chalcedony.  
Compared to Cuprite, CSVM performs better on Samson and Jasper Ridge and greatly improves the extraction accuracy. The different performance on different datasets has relation to the spectral contrast of endmembers in the datasets. Cuprite has spectrally similar endmembers coupled with the effects of spectral variability, bringing difficulties to accurate extraction [35].  
In conclusion, CSVM exhibits the best performance on endmember extraction, as it effectively alleviates the spectral variability. In addition, CSVM performs better for datasets with high spectral contrast of endmembers.