## 3 Results  
### Calibration Dataset  
Four different acquisitions have been done. A mosaic procedure, as already mentioned, was applied to obtain a single hypercube. After background removal the sample set was divided in two subsets (Figure 2), in order \"to define\" a calibration and validation dataset. The two subsets were utilized to perform calibration and validation, respectively. To optimize the identification of the asbestos in ACM, the dataset has been divided into four classes (i.e., asbestos, aggregates/mortar and brick, organic, fiberglass), as shown in Figure 2b. Classes have been selected according to spectra differences as resulting from PCA results as evidenced by PCA results [11]. The mean spectra of the selected classes (Figure 4) show the vibrational spectroscopic effects in the wavelength ranges of 1380-1400 nm (1 st OH overtone) and 2320-2340 nm (Fe-OH and Mg-OH combination band), indicating the presence in the sample/s of asbestos fibers [11; 12; 13; 14; 15; 16; 17; 18; 19; 20]. The selected acquisition resolution does not allow a spectral recognition of individual fibers. ACM spectral signatures are different in respect of C&DW uncontaminated materials. To improve separation between ACM and other C&DW materials, different preprocessing strategies were adopted to reduce light scattering and to emphasize spectral signatures. Rules 1 and 2 have adopted in order to perform a separation among the classes (AGGREGATES MORTAR AND BRIC + ACM) and the classes (FIBER GLASS + ORGANIC). Rules 3 and 4 allowed to perform a further two steps classification allowing to preliminary detect ACM and AGGREGATES MORTAR AND BRICK and a further \"refining\" allowing the identification, inside the previously recognized ACM class, of AGGREGATES MORTAR AND BRICK and ORGANIC, erroneously attributes (i.e., \"false positives2) to ACM class in rule 3. Error probably due to the lower size distribution of some AGGREGATES MORTAR AND BRICK and ORGANIC particles, in respect of those correctly identified. The adopted and applied preprocessing strategy were summarized in Table 1.  
Figure 4: Average spectra of the different classes selected as results of PCA application to samples constituting the calibration data set. Mean spectra of each class after pre-processing are shown in Figure 5. Finally, after preprocessing, dataset was analyzed by PCA (Figure 6). The first PCA (Figure 6a) shows significant difference between fiberglass and organic from other materials. The score plot shows, trough PC3, a separation of fiber glass and organic from aggregates \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Rule** & **Preprocessing** & \multicolumn{2}{c}{**Classification Output**} \\ \hline
1 & Standard Normal Variate (SNV) & \(\bullet\) & AGGREGATES MORTAR AND BRIC + ACM \\  & Mean Center (MC) & \(\bullet\) & FIBER GLASS + ORGANIC \\ \hline
2 & Mean Center (MC) & \(\bullet\) & FIBER GLASS \\  & Mean Center (MC) & \(\bullet\) & ORGANIC \\ \hline
3 & Standard Normal Variate (SNV) & \(\bullet\) & ACM \\  & 1 st Derivative \({}^{\star}\) Mean Center (MC) & \(\bullet\) & AGGREGATES MORTAR AND BRICK \\ \hline
4 & Standard Normal Variate (SNV) & \(\bullet\) & ACM \\  & and Smoothing \({}^{\star\star}\) & \(\bullet\) & AGGREGATES MORTAR AND BRICK \\  & Mean Center (MC) & \(\bullet\) & ORGANIC \\ \hline \hline \end{tabular} \({}^{\star}\) (order: 2, window: 33 pt and tails: polyinterp). \({}^{\star\star}\) (order: 0 and window: 11 pt).  
\end{table} 
Table 1: Description of the pre-processing strategies applied to the spectra of the different C&DW for each rule. Figure 5: Average preprocessed spectra considered to set up the rules in the developed hierarchical model obtained applying Standard Normal Variate (SNV) and Mean Center (MC) (rule 1) (**a**); MC (rule 2) (**b**); SNV and 1 st Derivative (order: 2, window: 33 pt, tails: polyinterp) and MC (rule 3) (**c**) and SNV and Smoothing (order: 0, window: 11 pt) and MC (rule 4) (**d**). mortar and brick. These features were used to define the rules of the hierarchical classification.