## 5 Principal Component Analysis (PCA)
Regarding PC1 of the failure dataset, the variables that contribute the most are C-MW, C-HAC, and \(\Delta\)PSA, while the variables that contribute the least are CnGC, C-AGC, and C-HBD. Regarding PC2, the variables that contribute the most are \(\Delta\)HAC, \(\Delta\)MW, and C-AGC, while the variables that contribute the least are \(\Delta\)AGC, \(\Delta\)CGC, and \(\Delta\)CnGC. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Success Dataset**} & \multicolumn{3}{c}{**Failure Dataset**} \\ \hline  & **PC1** & **PC2** & **PC3** & **PC1** & **PC2** & **PC3** \\ \hline Standard deviation & 2.26 & 1.83 & 1.18 & 2.41 & 1.97 & 1.72 \\ Proportion of variation & 0.32 & 0.21 & 0.09 & 0.31 & 0.21 & 0.16 \\ Cumulative proportion & 0.32 & 0.53 & 0.61 & 0.31 & 0.51 & 0.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: PCA results: Components distribution. The data presented in Table 6 can also be represented as bar graphs indicating the percentage contribution of each variable to the PC. Figures 5 and 6 depict the contribution of the variables as bar graphs. The contributions of each variable can also be represented as vectors, whose magnitude, direction, and angle provide insight into the behavior of the variable's contribution to the PC. Figure 7 depicts the contribution of the variables in vectors. In terms of the contribution and relationship between variables and their contribution to the PCA, variables with the most extended vectors contribute the most to the PC, whereas the magnitude of the angle between variables represents the correlation between variables; if the angle is slight, it indicates a positive, strong correlation between variables, indicating that they tend to vary together, whereas variables with a large angle between them have a low or negative correlation. Another factor is the direction of the respective vector, which indicates that the variable has an inverse relationship to the other variables and may have opposing effects on the PC [50; 51]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{5}{c}{**Success Dataset**} & \multicolumn{5}{c}{**Failure Dataset**} \\ \hline \multicolumn{2}{c}{**PC1**} & \multicolumn{2}{c}{**PC2**} & \multicolumn{2}{c}{**PC1**} & \multicolumn{2}{c}{**PC2**} \\ \hline
**Variable** & **Contribution** & **Variable** & **Contribution** & **Variable** & **Contribution** & **Variable** & **Contribution** \\ \hline \(\Delta\)MW & 17.67 & \(\Delta\)HBD & 22.65 & C-MW & 11.71 & \(\Delta\)HAC & 18.58 \\ AHAC & 17.37 & \(\Delta\)logP & 21.00 & C-HAC & 11.66 & \(\Delta\)MW & 17.44 \\ AHBA & 12.93 & \(\Delta\)PSA & 10.86 & APSA & 9.60 & C-AGC & 10.48 \\ AACC & 10.92 & AHGC & 9.14 & AHBD & 9.24 & C-CnGC & 9.57 \\ AHGC & 10.86 & AAGC & 7.22 & AHBA & 8.85 & C-HBD & 9.45 \\ APSA & 9.69 & \(\Delta\)CGC & 6.47 & C-CGC & 8.14 & C-PSA & 5.68 \\ \(\Delta\)CnGC & 6.59 & \(\Delta\)CnGC & 6.46 & AlogP & 6.80 & C-CCC & 4.83 \\ AGCGC & 5.54 & AHBA & 5.47 & AHGC & 6.65 & C-HCC & 4.78 \\ C-LogP & 4.50 & C-LogP & 5.47 & C-PSA & 4.53 & APSA & 4.00 \\ C-CGC & 2.54 & C-HBD & 2.88 & C-HGC & 3.86 & AHGC & 3.49 \\ AHBD & 0.42 & C-CnGC & 1.01 & \(\Delta\)CCC & 3.74 & C-LogP & 3.21 \\ C-ACC & 0.32 & AHAC & 0.59 & AAGC & 3.48 & AHBA & 2.37 \\ C-HGC & 0.32 & AMW & 0.27 & AMW & 2.93 & AlogP & 1.64 \\ C-HBD & 0.24 & C-AGC & 0.26 & C-CnGC & 2.53 & AHBD & 1.53 \\ C-CnGC & 0.10 & C-CCC & 0.18 & C-logP & 2.47 & C-MW & 1.29 \\ AlogP & 0.00 & C-HGC & 0.07 & AHAC & 1.72 & C-HAC & 1.24 \\  & & & \(\Delta\)CnGC & 1.06 & AAGC & 0.42 \\  & & & C-AGC & 0.62 & \(\Delta\)CGC & \(1.0\times 10^{-3}\) \\  & & & C-HBD & 0.41 & \(\Delta\)CnGC & \(1.2\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: PCA results: Variables contribution. Figure 5: Success dataset contribution of variables for PC. (- - -) Dashed line indicates that the variables whose values are above the line account for 30% of the total contribution of the PC. Figure 6: Failure dataset contribution of variables for PC.