## 3 Results and Discussion  
Seven different species of mycobacteria were investigated by HS-SPME-GC-MS, plus the medium for control purpose. Six biological replicates were analyzed for each class. Two replicates (one Avi and one medium) were lost due to a technical problem during sample preparation. Therefore, a total of 46 samples were used in the following analysis. Figure 1 shows a representative VOC total ion chromatogram profile for each species. The data matrix obtained after alignment, consisting of 879 total features, was first polished by removing common contaminants (e.g., siloxane and phthalates) and then reduced based on a frequency of observation (FOO) cutoff of 50% (i.e., features present in at least three out of six samples within one class were retained for further statistical evaluation), in order to retain the most consistent peaks, resulting in a final data matrix of 667 features. Prior to further statistical analyses, the relative abundance of compounds across chromatograms was normalized using Probabilistic Quotient Normalization (PQN) [23] and log-transformed [15]. On this data matrix, the Pearson's correlation coefficient was calculated to evaluate the correlation of the overall profile within the biological replicates (Figure 2). Average correlation coefficients within the same class were all above 0.70 (Abs: 0.77; Avi: 0.84; BCG: 0.77; Bol: 0.84; Chim: 0.85; Int: 0.73; Mas: 0.67) except for the Mas species which contained an outlier (Mas1, circled in red in Figure 2) was detected and removed. The removal of the outlier increased the correlation amongst the remaining Mas replicates, with a Pearson coefficient of 0.95. This Pearson test confirmed the high consistency of the sampling and measurements. To test for statistical significance, the Kruskal-Wallis (KW) test [24], with post-hoc Dunn test and Benjamini-Hochberg (BH) correction [25] to minimize the false discovery rate, was used. All features not significantly different (\(p\) > 0.05) between the different mycobacteria species and the medium were removed, obtaining a panel of 607 features. This panel was used for a first evaluation of the discriminatory capability of the VOC profile. The principal component analysis (PCA) obtained, along with the flowchart to reduce to the panel of 607 features, are reported in Figure 3. The PCA showed a rather low total variance of 38%. The discrimination between the groups was not very clear. Only the medium and the group of Bol were well separated from the others in the PCA space, while the other species were spread on the PCA space giving two different clusters: one containing Mas + Abs (bottom left of the PCA in Figure 3) and another big cluster containing the other four mycobacteria species, Avi + BCG + Chim + Int (the top-right of the PCA in Figure 3). Due to the high dimensional nature of -omics data, it is essential that machine algorithms are selected which can handle cases when the number of features far outweigh the number of samples [26]. Moreover, these algorithms need to also be able to handle highly correlated features (multicollinearity). In this context, to improve the discrimination capability of the overall classification, the random forest (RF) algorithm was applied to select and retain the most discriminatory features. RF is a machine learning algorithm that  
Figure 1: GC-MS total ion current (TIC) chromatogram obtained for the seven different mycobacteria and the medium. Abs—M. _abscessus_; Avi—M. _avium_; BCG—M. _bovis_; Bol—M. _bolletti_; Chim—M. _chimera_; Int—M. _intracellular_; Mas—M. _massiliense_; Media—growth media. works by generating many classification trees, using randomly selected subsamples of both features and data points. Features are ultimately selected based on which variables best divides the data according to class at each split [27]. A six-classes analysis was carried out. Features were ranked according to their mean decrease accuracy. In total, 13 features were selected to maximize the accuracy of the model (Table 1).