## 3 Results
### Reduction of Particle Geometry Parameters Using Correlation, PCA and CA Analysis
From the geometric component matrix (Table 4), the highest positive loadings of the first component regarding parameters defining particle size were 0.318 (L) and 0.308 (\(\overline{D}_{\text{F}}\)), with a negative loading of \(-0.318\) (P). High loadings, if positive, indicate what the component is, and, if negative, what it is not. It can also be observed that the other size parameters in component PC1 did not deviate significantly in the results. In the second component, the highest loading was 0.302 (W), while in the third component, no parameter regarding particle size stood out. When considering parameters defining particle morphology, the first component singled out compactness with a loading of 0.304. However, the loadings of other parameters on this component had close values. PC2 and PC3 again identified multiple parameters with loadings: 0.468 (El), 0.461 (AR), and 0.444 (RD) in the second component and 0.317 (RT) and 0.320 (AR) as positive loadings, and \(-0.381\) (CVX) and \(-0.466\) (SLD) as negative loadings in the third component. The relationship between the first two components is depicted in the biplot (Figure 10). components around the set of original data. In this particular case, three components were rotated using orthogonal varimax rotation, which maximised the sum of variances of squared factor loadings. Table 5 presents the factor loadings for each variable after rotation. The results of the cluster analysis of particle geometric parameters are illustrated by the dendrogram in Figure 11. A shorter distance between clusters indicates a stronger correlation between variables. Size parameters remained grouped in one cluster, demonstrating the strongest correlation among these sizes. The second cluster consists of parameters such as circularity, compactness, convexity, and rectangularity. The third cluster identifies parameters such as roundness, elongation, and aspect ratio, defining the particle form, and they are separated into a distinct group, similar to the PCA analysis. The fourth cluster singles out solidity as a distinct parameter defining the morphological roughness of the particle. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Geometric Parameters**} & \multicolumn{3}{c}{**Components**} \\ \cline{2-4}  & \(\quad\)**PCI** & \(\quad\)**PC2** & \(\quad\)**PC3** \\ \hline \(A\) & \(-0.295\) & \(0.288\) & \(-0.216\) \\ \(P\) & \(-0.318\) & \(0.151\) & \(-0.111\) \\ \(\overline{D}_{F}\) & \(0.308\) & \(-0.183\) & \(0.173\) \\ \(L\) & \(0.318\) & \(-0.115\) & \(0.177\) \\ \(W\) & \(-0.285\) & \(0.302\) & \(-0.077\) \\ \(D_{CE}\) & \(-0.294\) & \(0.230\) & \(-0.222\) \\ \(El\) & \(0.154\) & \(0.468\) & \(0.297\) \\ \(RT\) & \(-0.282\) & \(0.016\) & \(0.317\) \\ CVX & \(0.264\) & \(0.051\) & \(-0.381\) \\ \(Circ\) & \(0.292\) & \(0.174\) & \(-0.273\) \\ \(AR\) & \(0.148\) & \(0.461\) & \(0.320\) \\ \(RD\) & \(0.190\) & \(0.444\) & \(0.231\) \\ \(SLD\) & \(0.198\) & \(0.254\) & \(-0.466\) \\ CP & \(0.304\) & \(0.088\) & \(-0.248\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: PCA of geometric parameters. Figure 10: Biplot of principal component analysis of geometric parameters of the sample.