## 3 Results and Discussions
### Chemometric Analysis of FTIR Data  
Most of the time, it is very difficult to determine the components present in the structure of the paper medium, in the pigments used to produce inks or in degradation products by spectral analysis [42]. FTIR spectra contain information that can be collected by statistical multivariate techniques. Thus, the differences between several similar spectra can be determined, and the chemometric analysis of the spectral data allows the extraction of additional data that bring about new information that is prone to interpretation [16; 43].  
PCA (Principal Component Analysis) based on the spectra acquired by FTIR spectroscopy was used to determine sample variability (Figure 11).  
As far as the data in the FTIR spectrum are concerned, the main component 1, represented on axis X in Figure 12, accounts for 56.3% of the variance (variability), while the main component 2, represented on axis Y, accounts for 32.7% of it. The determination coefficient R\({}^{2}\) was also calculated for the first 3 main components (Figure 13).  
Figure 11: Variance percentage accounted for by the main components for the data in the IR spectrum.  
Figure 10: FT-Raman spectra for ink: (a) S1; (b) S2; (c) S3.  
The determination coefficient specifies how much of the variation of one variable is accounted for by the variation of the other variable (indicates the percentage of the total variation of the dependent variable that is accounted for by the independent variable). The correlation between samples is high when R\({}^{2}\) is as close as possible to the unit (greater than 0.85), in our case (Figure 13) at 1500 cm\({}^{-1}\), within the 2000-3000 cm\({}^{-1}\), 3500 cm\({}^{-1}\) range.  
A cluster analysis method was used to determine the links between the samples. The small number of samples (\(n=10\)) determined the use of a non-hierarchical method, which is based on shifting observations from one group (cluster) to another during the analysis. The k-means method, implemented in R through the'stats' package, is the most common. It starts from a random division of observations into k groups (clusters). For each stage, a mean of each group is calculated, and the items are shifted to the group whose mean is closest to them, until each item is part of the group with the closest mean (i.e., with characteristics as similar as possible), that is until no item needs shifting [44].  
A shortcoming of the k-means method and of non-hierarchical methods, in general, is the need to specify a number of clusters by the initiator. When the number of clusters is not known in advance by objective criteria, it may be estimated by heuristic methods that help the initiator to choose the spot where a balance is struck between the degree of similarity between the items and the degree of generalization of the classification. In this case, we used the elbow method, which is based on determining an inflection point, and the silhouette method, which involves determining a value that expresses how similar an  
Figure 12: PCA of individual observations for the data in the FTIR spectrum: 1—G1; 2—G2; 3—G3; 4—I1; 5—L1; 6—L3; 7—I2; 8—L2; 9—I3; 10—I4.  
Figure 13: Determination coefficient R\({}^{2}\) for each main component.  
item is to the group (cluster) to which it belongs compared to other clusters. Considering the results of these methods, four clusters were used (Figure 14).  
We found that the Loebell document samples (5, 6, 8) formed a separate cluster (cluster 3), suggesting the existence of special paper characteristics, which is not the case with the Istrati and Gherman documents, which were grouped together in clusters 2 and 4. Sample 7 (I2) was also a separate cluster.