## 3 Results and Discussion
### Principal Component Analysis of Volatile Compounds  
Volatile compounds identified via GC-MS among the different probiotic, symbiotic, and control yogurt samples (S1-C: control plain yogurt; S2-P: yogurt with _S. boulardii_; S3-Syn1: yogurt with _S. boulardii_ + 1% inulin; S4-Syn1.5: yogurt with _S. boulardii_ + 1.5% inulin; and S5-Syn2: yogurt with _S. boulardii_ + 2% inulin) during four weeks of storage were further analyzed via principal component analysis (PCA) and hierarchical cluster analysis (HCA). Both these multivariate statistical techniques were used for easy interpretation of the volatile compounds' data from GC-MS. Hierarchical cluster analysis is shown in Figure 1, in which the yogurt samples are divided into three groups, determined by the average linkage among different groups based on Euclidian distance. The principal component analysis explained a total of 96.7% variance, to which principal component 1 (PC1) contributed 90.3%, whereas principal component 2 (PC2) contributed 6.4%, respectively.  
Two principal components were used in most cases of PCA analysis, appropriately explaining a great proportion of variations in original parameters. A bi-plot of different yogurt sample scores is shown in Figure 2, revealing the most important loadings and  
Figure 1: Hierarchical cluster analysis of different yogurt samples on the basis of volatiles produced during storage of four weeks.  
the percentage accounted for by the two first principal components (PC1 and PC2) after analysis. There were three different groups, and the samples were positioned based on the concentrations of volatiles and storage weeks. All yogurt samples were positioned on the left side of PC1, but group1 (S1-C and S2-P) were in the negative part of the bi-plot in week 0. The control samples remained in the negative zone throughout the four weeks of storage, having very few volatiles produced. Group 2 samples having probiotic and symbiotic yogurt samples were positioned on the positive side of PC1, especially after 1 week of storage. Samples in group 3 (synbiotic only having both _S. boulardii_ and inulin) were positioned on the positive side of PC1 and located together in the bi-plot. Significant differences were observed among old yogurts of these groups at weeks 0 and 4. In summary, the bi-plot indicates that limonene, L-limonene, and carboxylic acids (octanoic acids, hexanoic acid, butanoic acid, and acetic acid), along with ethanol, were grouped on the positive side of PC1, strongly contributing to the flavor of probiotic and symbiotic yogurt samples. Similarly, esters (1-butanol-3-methyl-acetate, butanoic acid-3-methyl butyl ester, octanoic acid ethyl ester) were secondary in contributing to the flavor of probiotic and symbiotic yogurt samples and were also placed on the positive side of PC1. The remaining volatile compounds (propanoic acid and 2-methyl-butanoic acid, 3-hydroxy butanal) were grouped in the center of the bi-plot, with less contribution to the principal component, compared with the other compounds. According to these results, PCA, along with HCA, is a powerful tool to distinguish the samples based on treatment (probiotics, synbiotics) and magnitude of storage time.