# Quadratic Clustering-Based Simplex Volume Maximization for Hyperspectral Endmember Extraction
## 3 Results and Discussion
### Results for Abundance Estimation  
To evaluate the performance of all algorithms on abundance estimation, the endmembers obtained by these algorithms are adopted to generate abundance maps through the FCLS algorithm. RMSE is calculated between the estimated abundance vector and ground-truth abundance vector. The results are shown in Table 2. Because there are no ground-truth abundance maps for Cuprite, only Samson and Jasper Ridge are used in this section. It is noted that the unmixing result is an indirect verification of EEAs, as it also relies on the abundance estimation algorithm.  
From the results, CSVM obtains the best RMSE on soil and the best average for Samson. For Jasper Ridge, CSVM provides the best RMSE on tree, water and road and the best average. It indicates that the endmembers extracted by CSVM reduce the error of abundance estimation.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & & \\ \hline
**EEAs** & **VCA** & **SGA** & **AVMAX** & **MVSA** & **AMEE** & **ECSO** & **KMEE** & **FSPM** & **SENMAV** & **SPEW** & **CSVM** \\ \hline Soil & 0.0404 & 0.0404 & 0.0404 & 0.0821 & 0.2853 & 0.0404 & 0.0404 & 0.0207 & 0.0404 & 0.0404 & **0.0109** \\ Tree & **0.0219** & 0.0407 & 0.0548 & 0.0489 & 0.0449 & 0.0713 & 0.4319 & 0.0495 & 0.0407 & 0.0407 & 0.0227 \\ Water & 0.1126 & 1.1483 & 0.1295 & 0.3712 & 0.2513 & 0.1552 & 0.1553 & 0.1299 & 0.1855 & 0.1305 & **0.0202** \\ Average & 0.0583 & 0.4098 & 0.0749 & 0.1674 & 0.1938 & 0.0890 & 0.2092 & 0.0667 & 0.0889 & 0.0705 & **0.0179** \\ \hline \multicolumn{11}{c}{**Jasper Ridge**} \\ \hline
**EEAs** & **VCA** & **SGA** & **AVMAX** & **MVSA** & **AMEE** & **ECSO** & **KMEE** & **FSPM** & **SENMAV** & **SPEW** & **CSVM** \\ \hline Tree & 0.1559 & 0.1559 & 0.1559 & 0.1837 & 0.1173 & 0.2030 & 0.0950 & 0.1979 & 0.1180 & 0.1686 & **0.0262** \\ Water & 0.2494 & 0.8953 & 0.2453 & 0.4035 & 0.1190 & 0.2540 & 0.7566 & 0.2399 & 0.2453 & 0.2430 & **0.0757** \\ Soil & 0.1336 & 0.1336 & 0.1336 & 0.2169 & 0.1302 & 0.1632 & 0.2299 & 0.2263 & 0.1353 & 0.1257 & **0.1231** \\ Road & 0.1069 & 0.1069 & 0.1069 & 0.3523 & 0.9162 & 0.2300 & 0.1792 & 0.1792 & 0.0443 & 0.0443 & **0.0148** \\ Average & 0.1614 & 0.3229 & 0.1604 & 0.2891 & 0.1957 & 0.2125 & 0.3152 & 0.2108 & 0.1357 & 0.1454 & **0.0599** \\ \hline \multicolumn{11}{c}{**Cuprite**} \\ \hline
**EEAs** & **VCA** & **SGA** & **AVMAX** & **MVSA** & **AMEE** & **ECSO** & **KMEE** & **FSPM** & **SENMAV** & **SPEW** & **CSVM** \\ \hline Alunite & 0.1023 & 0.0846 & 0.0846 & 0.1213 & 0.1062 & 0.0919 & 0.0919 & **0.0834** & 0.0919 & 0.1194 & 0.0931 \\ Andradite & 0.0880 & 0.0879 & 0.0706 & 0.1712 & 0.0817 & 0.0682 & 0.0658 & **0.0636** & 0.0717 & 0.0907 & 0.0698 \\ Buddingtonite & **0.0711**Therefore, compared with other EEAs, our method achieves better performance in hyperspectral unmixing considering endmember extraction and abundance estimation, comprehensively.  
Figures 14 and 15 demonstrate the comparison between estimated abundance maps using endmembers extracted by CSVM and the ground truth. As is shown in absolute error maps, CSVM obtains smaller estimation error on endmembers in Jasper Ridge than that in Samson, which means CSVM performs better on Jasper Ridge than on Samson. In addition, the results on both datasets show that the absolute error is large in areas with complex ground objects distribution, especially in the transition areas with different land cover types on both sides.