## 5 Principal Component Analysis (PCA)  
PCA is one of a series of approaches for representing high-dimensional data in a lower-dimensional, more manageable format without sacrificing too much information. PCA is one of the most straightforward and reliable dimension-reduction techniques. It is  
Figure 4: Kendall correlation matrices. **(a)** Success dataset. **(b)** Failure dataset. Figure 3: Pearson correlation matrices. **(a)** Success dataset. **(b)** Failure dataset. also one of the oldest and has been repeatedly rediscovered in other domains; therefore, it is also known as the Karhunen=-Loeve transformation, the Hotelling transformation, the method of empirical orthogonal functions, and singular value decomposition [49]. In this manner, a PCA was performed on each dataset (success and failure) by a singular value decomposition of the centered and scaled data matrix (mean 0, variance 1) and by not using eigen on the covariance matrix [50]; the obtained results are presented in Table 5.  
PCA transformed the original variables into a set of principal components (PCs) by reducing the dimensionality of the variables and identifying patterns and structure in multivariate datasets [42]. The standard deviation quantifies the dispersion or spread of the data along each PC; more significant standard deviation values indicate a greater spread along the respective PC. In contrast, the variation proportion represents the total variability in the data explained by each principal component, with larger values indicating that the respective PC captures a more significant amount of variability in the data. Lastly, the cumulative proportion represents the cumulative amount of total variation explained by a set of PCs; this value provides insight into the total amount of variation captured by a combination of PCs, where higher cumulative proportion values indicate that these principal components explain a more significant proportion of the total variation in the data [42; 50; 51]. PC1 has the most significant standard deviation across both datasets, indicating that it captures the most data variability. PC1 explains 32% total variation in the success data and 31% in the failure data, according to the relatively high proportion of variation values for PC1. The cumulative proportion for PC1 demonstrates that it alone accounts for a significant portion of the total variation, indicating its importance in describing the overall patterns and structure of the data. PC2 has a lower standard deviation than PC1 in both datasets, indicating that it captures less variability but is still statistically significant. Despite being smaller than PC1, the PC2 proportion of variation values is still significant, indicating that PC2 explains the additional 21% of the variation in both datasets. The PC2 cumulative proportion demonstrates its contribution to capturing additional variation, enhancing the PC1 representation of the data. PC1 and PC2 represent 32% and 21% of the values, respectively, for a total coverage of 53% and 51% of the data in the success and failure datasets. PC3 has the lowest standard deviation of all principal components in both datasets, indicating that it captures the slightest variance. PC3 explains less variation than PC1 and PC2 because its proportion of variation values is the lowest. PC3 contributes to capturing additional variation, albeit to a lesser extent than PC1 and PC2. Table 6 displays the contribution of each variable to PC1 and PC2 for the success and failure datasets. With respect to the PC1 of the success dataset, MW is the variable that contributes the most to PC1, followed by \(\Delta\)HAC and \(\Delta\)HBA. C-HBD, C-CnCG, and \(\Delta\)logP are the variables that contribute the least to PC1. Referring to PC2, HBD is the variable that contributes the most, followed by \(\Delta\)logP and \(\Delta\)PSA, while C-AGC, C-CGC, and C-HGC contribute the least.