## 3 Results and Discussion
### Relating Samples to VOCs by CoDa Exploratory Analysis
#### 3.5.2 Relating Samples and VOCs by Clustering  
The dissimilarity between the VOC profile of spoiled and normal samples was also studied by clustering, a technique successfully used for segregating according to starter culture [6]. The technique was applied to the _clr_ transformed data set (_clr coefficients_), using the function WARD from easyCoDa with the unweighted and weighted options (Figure 6). The VOC profiles of the butyric spoiled brines (F282 and F283) were always consistently recognised as singular and different from any other sample. The association agrees with that observed in the CoDa biplot (Figure 5). Besides, regardless of the option, putrid (F562) and normal (F592) samples from industry B were also considered alike, possibly because of the early initial stage of the spoilage in the first. The grouping agrees with the ANOVA results where F562 had a limited contribution to most VOCs models. However, the segregation between sulfidic and normal/putrid samples from industry B and grouping normal samples depended on the cluster option. In the unweighted cluster (Figure 6A), F562, F592, and F508 (sulfidic) from industry B (F562, F592, and F508) were grouped, although considering sulfidic sample (F508) somewhat different; on the contrary, in the weighted option (Figure 6B), segregation of sulfidic sample from the other two samples from industry A was straightforward and more reasonable. In addition, clustering normal processes in the unweighted option grouped those from industry A (including F502, from industry B) separately from industry B. In the weighted dendrogram, they were included together and considered relatively close. Figure 4: Tetrahedral centered plot of samples as function of the four VOCs with the highest _clr_ variance (methyl butanoate (V13), ethyl butanoate (V18), 6-hepten-1-ol (V55), and butanoic acid (V62)). Figure 5: CoDa biplot of the VOCs and samples. Projections on the planes 1 st vs 2 nd (**A**) and 1 st vs 3 rd (**B**) dimensions. Symbols of samples correspond to industry A (F282 and F283, affected by butyric; F284, F285, F286, and F309, normal fermentations) and industry B (F508 and F562, sulfidic and putrid spoilage, respectively; F502 and F592, normal fermentations). Symbols for VOCs are detailed in Table S1 and S2, and S3. _clr_ stands for _clr coefficients_. The same easyCODA function was applied for detecting groups of VOCs (Q-Q clustering) which could be related to specific spoilages. The difference between the unweighted and weighted options was marked (Figure 7), showing the first a greater degree of dissimilarity and more challenging interpretation. Both options agree to segregate cluster C1 on the left composed of butanoic acid (V62), ethyl butanoate (V18), and methyl butanoate (V13), significantly related to the two samples (F282 and 283) affected by the butyric spoilage (Supplementary Table S2). Figure 6: Clustering of samples, based on _clr coefficients_, using the WARD function from easyCODA and the unweighted (**A**) and weighted (**B**) options. Symbols of samples correspond to industry A (F282 and F283, affected by butyric spoilage; F284, F285, F286, F309, normal fermentation) and industry B (F508 and F562, sulfidic and putrid spoilage, respectively; F502 and F592, normal fermentations). Regarding the unweighted option, C2 cluster included highly significant and almost exclusive compounds associated with the ANOVA to sample F282 (affected by the butyric spoilage) (Table S2). Similarly, most of the VOCs grouped into cluster C7 were characterised by the exclusive significant-high contribution of F508 (affected by sulfidic spoilage) to their ANOVA models. Besides, (Z)-3-hexen-1-ol (V47) was present in all the samples and dimethyl sulfoxide in all except in F282 and F283. Among the compounds included in cluster C8, only D-limonene (V32) was exclusively related to F562. The rest of the components were mainly linked by the ANOVA to sample F562 (putrid) and other samples.