## 4 Results  
The application of DS on the selected bands and the PCs of the three datasets reduced the correlation among the SWIR bands and the NIR bands. Resultantly, the PCs represented more contrasting features in the data, as seen from the scatter plots (shown in Figure 4) of PC1, PC2, and PC3 of the Landsat-8 OLI data. FPCS performed after DS showed relatively better results than the FPCS on raw data; therefore, the final FCC had two components from stretched data, i.e., Sentinel-2 and Landsat-8, and one component from raw data, i.e., Landsat-8. The eigen analysis of all data sources revealed a correlation between the eigenvector loadings and the spectral ranges being absorbed/reflected in the PCs. The spectral characteristics of granite were used to identify suitable PCs by analyzing the amount of information from the SWIR and TIR bands in each component and by the visual comparison of the PCs and their associated eigenvector loadings. The spectral information about the vegetation, granite, and marble was obtained through GEE's ui.chart feature.  
Since the number of bands in the multispectral data was limited, the spectral profile showed smooth variations (as it interpolated the spectral profile between two known points) in Figure 5. The plots of different mineral components of granite compositions of case studies from the USGS spectral library are shown in Figure 6. The eigenvector loadings from the application of FPCS to the stretched and unstretched (raw) Sentinel-2, Landsat-8 OLI, and TIRS in ASTER (shown in Figures 7-9) are reported in Tables 2-4.  
Several PCs that mostly retained topographical or vegetation responses and no discriminative spectral response of granite and marble were ignored. Key FPCS components were selected from Tables 2-4 based on the absolute loadings of critical bands responding to different associated minerals.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Landsat-8**} & \multirow{2}{*}{\begin{tabular}{c} **NIR Band 5** \\ **(850–880 nm)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **SWIR1 Band 6** \\ **(1570–1660 nm)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **SWIR2 Band 7** \\ **(2110–2290 nm)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **TIR1 Band 10** \\ **(10,600–11,190 nm)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **TIR2 Band 11** \\ **(11,500–12,510 nm)** \\ \end{tabular} } \\ \hline \multirow{2}{*}{\begin{tabular}{c} **TIR1** \\ **(850–12,510 nm)** \\ \end{tabular} } & Raw & 0.095 & \(-\)0.125 & \(-\)0.243 & 0.675 & \(-\)0.679 \\ \cline{2-6}  & Str & 0.561 & 0.621 & 0.470 & 0.230 & 0.163 \\ \hline \multirow{2}{*}{\begin{tabular}{c} **TIR2** \\ **(850–880 nm)** \\ \end{tabular} } & Raw & 0.858 & 0.178 & 0.120 & 0.308 & 0.351 \\ \cline{2-6}  & Str & 0.805 & \(-\)0.262 & \(-\)0.484 & \(-\)0.176 & \(-\)0.133 \\ \hline \multirow{2}{*}{\begin{tabular}{c} **TIR1** \\ **(850–12,510 nm)** \\ \end{tabular} } & Raw & 0.127 & \(-\)0.675 & \(-\)0.707 & \(-\)0.053 & \(-\)0.163 \\ \cline{2-6}  & Str & \(-\)0.020 & 0.247 & 0.258 & \(-\)0.792 & \(-\)0.496 \\ \hline \multirow{2}{*}{\
\begin{tabular}{c} **TIR2** \\ **(850–12,510 nm)** \\ \end{tabular} } & Raw & 0.329 & \(-\)0.591 & \(-\)0.643 & \(-\)0.358 & 0.030 \\ \cline{2-6}  & Str & 0.191 & \(-\)0.696 & 0.692 & 0.007 & \(-\)0.005 \\ \hline \multirow{2}{*}{
\begin{tabular}{c} **TIR3** \\ **(850–12,510 nm)** \\ \end{tabular} } & Raw & \(-\)0.362 & \(-\)0.385 & \(-\)0.116 & 0.565 & 0.623 \\ \cline{2-6}  & Str & \(-\)0.009 & 0.021 & 0.011 & 0.538 & \(-\)0.843 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Eigenvector loadings after applying feature-oriented principal component selection (FPCS) to raw (Raw) and stretched (Str) Landsat-8 Operational Land Imager (OLI) and Landsat-8 Thermal Infrared Band Sensor (TIRS) data. The highlighted components were used in generating the final image shown in Figure 10a.  
Figure 6: USGS spectral library plots of different granite minerals found in the case studies.