## 4 Results and Discussion
### PCL-GO Dataset  
The obtained map of the PCL-GO 3D printed composites is composed of 51 \(\times\) 25 pixels with 1015 spectral bands between 996 cm\({}^{-1}\) and 2111 cm\({}^{-1}\). To reduce the dimensionality of and to project the data into a linear subspace, the PCL-GO map has been processed through an AANN. Following an iterative process varying the number of nodes in the hidden layers, it has been found that the best topology, having the lowest training MSE presented a 1015-500-25-500-1015 topology. This means that the AANN has the 1015 bands as the input, 500 nodes in the coding/decoding layer, and then 25 nodes in the bottleneck layer. The features obtained through the bottleneck layer have then been used as input to the N-FINDR algorithm considering only two endmembers. Subsequently, the obtained endmembers have been used to determine the fractional abundances in each pixel of the map. The obtained results have been compared with those collected using the classical linear unmixing approach, without the projection in the feature space. Analyzing Figure 4, showing the reference spectra and the endmembers resulting from the linear approach, it is possible to note that while the first endmember, noted as EM#1, is very similar to the PCL reference spectra, the second endmember, noted as EM#2, presents spectral characteristics more similar to a mixed spectrum rather than pure GO. This can be clear comparing the response of features 18, 21, and 25 reported in Figure 5.  
Table 1 reports the SAD values obtained comparing the reference spectra of GO and PCL, projected in the feature space, with the endmembers obtained with both linear and nonlinear approaches, respectively. Referring to the linear approach, the SAD values for EM#2 present almost the same value for the comparison with PCL and GO. This means that using the linear approach is not possible to clearly associate EM#2 to any reference spectra. On the other hand, considering the nonlinear approach, the SAD values for EM#1 is lower when compared to PCL, while EM#2 present the lower value when compared to GO, allowing the association of the two derived endmembers to the two materials. For sake of comparison, following a traditional approach, we also estimated the similarities of detected spectra with a reference spectral library in terms of SAD values. Figure 6 reports the comparisons between the GO and PCL spectra and the most similar spectra in terms of SAD. As can be noted, this approach is possible to identify correctly only PCL, which is the dominant material. Indeed, this approach fails to identify GO mainly because it is present only in mixed solutions. \begin{table}
\begin{tabular}{c c c c c} \hline \multicolumn{5}{c}{**Linear Unmixing Approach**} & \multicolumn{2}{c}{**Nonlinear Unmixing Approach**} \\ \hline  & GO & PCL & GO & PCL \\ \hline EM\#1 & 73.54 & 67.92 & 0.0028 & 0.0012 \\ \hline EM\#2 & 69.15 & 69.93 & 0.0015 & 0.0033 \\ \hline \end{tabular}
\end{table} 
Table 1: SAD values obtained by comparing the reference spectra of GO and PCL, and the endmembers obtained using the linear and nonlinear approaches. Figure 5: Reference features obtained projecting the reference spectra in the feature space, and the endmembers obtained with the proposed nonlinear approach. In a second evaluation the reference features, obtained from the projection of the reference spectra in the feature space have been used as endmembers to determine the fractional abundances of each pixel. The RMSE values have been derived by evaluating the errors between the original map and the reconstructed map obtained with Equation (9), where \(\Phi_{\mathrm{z}}(\mathrm{i,j})\) and \(\mathrm{E}_{\mathrm{z}}\) are respectively the endmembers and the fractional abundances obtained using the linear unmixing approach on the original data.