## 3 Results and Discussion
### Cluster Analysis  
A hierarchical cluster analysis and constellation plot were performed to identity analogies of the effects of by-products on the properties of the bread (Figure 4). The constellation plot consisted of four clusters. Group A included one cluster (C1) containing only the wheat control bread, and group B included three clusters: C2 (gluten-free control bread), C3, and C4 (gluten-free bread containing different by-products). The C3 cluster contained the highest counts of similar bread. The similarity between DTP, DPP, DPPP, and DPPSP at the additive levels of 5% and 7.5% was observed in the C3 cluster and the gluten-free bread with the addition of DOP, DAP, and DPPPS at the 2.5% additive level in the C4 cluster. The wheat control bread and gluten-free control bread differed highly from those with all samples containing by-products. The wheat control bread was characterized by higher values of Vsp, average size, perimeter, H\({}_{\rm m}\), h, Tx, and R\({}_{\rm CO2}\), and the control gluten-free bread was characterized by a long time at the maximum height of dough T\({}_{1}\), a high value of V\({}_{\rm 1 CO2}\), and a low value of Vs, average size, H\({}_{\rm m}\), and R\({}_{\rm CO2}\) (Figure 5). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Number of Cells/mm\({}^{2}\)**} & \multicolumn{2}{c}{**Average Cell Size (mm\({}^{2}\))**} & \multicolumn{2}{c}{**Area Fraction (\%)**} & \multicolumn{2}{c}{**Perimeter**} & \multicolumn{1}{c}{**Circularity**} & \multicolumn{1}{c}{**Solidity**} \\ \hline
**WheatCTRL1** & 0 & 203 \(\pm\) 8\({}^{\rm\,\,\,bd}\) & 1.672 \(\pm\) 0.26 \({}^{\rm\,\,\,a}\) & 18.25 \(\pm\) 1.34 \({}^{\rm\,\,a}\) & 4.32 \(\pm\) 0.27 \({}^{\rm\,\,a}\) & 0.81 \(\pm\) 0.007 \({}^{\rm\,\,\,i}\) & 0.85 \(\pm\) 0.006 \({}^{\rm\,\,f}\) \\ \hline
**GFCTRL 2** & 0 & 239 \(\pm\) 13\({}^{\rm\,\,abc}\) & 0.46 \(\pm\) 0.12 \({}^{\rm\,\,cde}\) & 12.85 \(\pm\) 3.18 \({}^{\rm\,\,bc}\) & 2.28 \(\pm\) 0.29 \({}^{\rm\,\,defl}\) & 0.87 \(\pm\) 0.01 \({}^{\rm\,\,defl}\) &  
Figure 4: Constellation plot and hierarchical clustering of the investigated wheat and gluten-free bread samples based on the Ward method (level increase: orange, level decrease: green). DOP: dried orange pomace; DAP: dried apple pomace; DTP: dried tomato peel; DPP: dried pepper peel; DPPP: dried prickly pear peel; DPPSP: dried prickly pear seed peel; CTRL: control; GF: gluten-free. Figure 3: Crumb appearance of wheat bread and gluten-free bread with and without added by-products. DOP: dried orange pomace; DAP: dried apple pomace; DTP: dried tomato peel; DPP: dried pepper peel; DPPSP: dried prickly pear seed peel; CTRL: control; GF: gluten-free; V_sp_: specific volume. Multivariate Analysis of the Rheofermentometer and Rheological Parameters of Dough and Bread Quality  
Figure 6a presents the correlation circle obtained from the principal component analysis on the rheofermentometer and the rheological parameters of dough and bread qualities measured in wheat and gluten-free samples. The first and second principal components justified 49.3% of the variability. Variables with high eigenvectors on principal component 1 were Tx, H\({}_{\text{m}}\), average size, perimeter, h, Vsp, H\({}^{\prime}\)m, and \(L^{*}\) crumb (Figure 6a). On PC1, Tx, H\({}_{\text{m}}\), average size, perimeter, h, and Vsp were negatively correlated with H\({}^{\prime}\)m and highly significant (\(p<0.001\)) and positive correlations were noted between H\({}_{\text{m}}\) and h (r = 0.94), followed by the Tx and H\({}_{\text{m}}\) pairs (r = 0.89), Tx and h (r = 0.89) and H\({}_{\text{m}}\) and Vsp (r = 0.81). Variables with high eigenvectors on principal component 2 were W, WL, \(L^{*}\) crust, T\({}_{1}\), pH, and H\(\%\). Negative correlations were observed between variables W and WL with \(L^{*}\) crust, T\({}_{1}\), and pH. Highly significant (\(p=0.001\)) and negative correlations were found between pH and WL (r = \(-0.67\)), T\({}_{1}\) and \(\%\) (r = \(-0.62\)), and T\({}_{1}\) and \(W\) (r = \(-0.67\)).