## 3 Results and Discussion
### Relationship of Relevant VOCs and spoilage by Heatmap  
The overall linkage of the previously associated with spoilages' VOCs and the samples was obtained by a heatmap, using their _clr coefficients_ (Figure 10).  
Figure 9: Biomarkers identified using the [PERSON] et al. [22] test. Plots correspond to, (**A**) spoiled butyric samples (F282 and F283) vs normal samples (F284, F285, F286, and F309) from industry A; (**B**) sulfidic (F508) vs normal samples (F502 and F592) from industry B; and (**C**) putrid (F562) vs normal samples (F502 and F592) from industry B. See text for correspondence between VOC indexes and their names. V*statistic stand for the standardized [PERSON] et al. [22].  
In industry A, the row dendrogram considered different F282 (R1) and F283 (R2), affected by butyric spoilage, although they have in common several compounds. These were (left to right) butanoic acid (V62), benzoic acid (V91), methyl salicate (69), ethyl butanoate (V18), methyl butanoate (V13), and styrene (V36). Nevertheless, each of these samples were also associated with specific VOCs. F282 (R1) was characterised by the additional presence of 1,4-dimethoxobenzene (V67), methyl propanoate (V8), (E)-3-hexen-1-ol (V46), pentanoic acid (V68), butyl propanoate (V34), propyl butanoate (V27), ethyl pentanoate (V29), methyl pentanoate (V23), and butyl acetate (V21). F283 (R2) was individually linked to ethyl lactate (V44), benzaldehyde (V56), (Z)-3-hexenyl acetate (V40), and ethyl hydrocinnamate (V79). The other normal fermentations (F284, F285, and F286, F309) were grouped in R7, and their VOC profiles were almost plain in the heatmap (based on compounds selected because of their relationship with spoilages), except for the presence of (E)-2-hexen-1-ol (V48), in F285 and F286, or octanoic acid (V85), in F286 (Figure 10).  
Regarding samples from industry B, F508 (R6) was again considered different from the other samples from this company (R8). However, notice the inclusion of F502, F562 (only incipient putrid spoilage), and F592, and the normal samples from industry A in  
Figure 10: Heatmap based on only those VOCs associated with spoilages by at least one previous statistical technique. 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).  
cluster R5, recognising such grouping the common characteristics associated with normal fermentations. F508 (R10), affected by sulfidic spoilage, was characterised in exclusive by 2-propyl-1-pentanol (V53), 2-methyl-2-butenal (V24), 2-methyl-3-buten-2-ol (V19), 2-pentanone (V11), isobutanol (V25), methanol (V6), dimethyl sulfide (V2), ethanol (V10), acetone (V3), isopentanol (V33), and 2-methylbutanal (V9). This association agrees with those from the ANOVA. The F508 (sulfidic spoilage) also shared 1,4 dimethoixbenzene (V67) with F282 (butyric). F502 (R9) was also separated from F562 and F592 (R10) and had a weak relationship with any compound related to spoilage. Its segregation agrees with various of the previous plots (Figure 6A). F562 (affected by initial putrid spoilage) and F592 were included in the same cluster (R10), which were associated with an almost plain VOC profile. However, F562 was particularly linked to 2-pentanol (V28), which could then be related to its detected (initial) putrid spoilage.  
Heatmap had the advantage of combining clustering of both cases and variables and then associating groups relatively similar, circumstance that allows a more straightforward comparison of the relationships between samples and VOCs.