## 4 Discussion
For the QDA model, the common feature is ACC344. This feature denotes the cross-covariance between \(E3\) and \(E4\) at \(L=4\), reflecting the relationship between amino acid occurrence in \(\alpha\)-helices and the relative frequency of amino acids within a defined interval. For the RF model, no standard features are identified by either technique. For the XGBoost model, the standard features are ACC111 and ACC123. ACC111 quantifies the auto-covariance of \(E1\) descriptors of adjacent amino acids, revealing crucial associations among their hydrophobicity. ACC123 demonstrates the cross-covariance between the hydrophobicity and molecular size of amino acids at \(L=3\). Next, we identified common attributes for two or three models using one of the feature importance techniques (Figure 2). ACC344 is common to both the QDA and RF models for the permutation feature importance technique, while ACC111 is common to both the RF and XGBoost models. The interpretations of these features have already been discussed. Another common attribute identified by this technique for the QDA and XGBoost models is ACC131, which represents the cross-covariance between the hydrophobicity and propensity of adjacent amino acids to occur in \(\alpha\)-helices at \(L=1\). The drop-column feature importance technique reveals no standard features for the QDA and XGBoost models. However, for the RF and XGBoost models, it identifies three standard features: ACC441, ACC415, and ACC443. ACC441 represents the auto-covariance between the relative frequency of adjacent amino acids, ACC415 denotes the cross-covariance between the relative frequency of the amino acids and their hydrophobicity at \(L=5\), and ACC443 signifies the auto-covariance between the relative frequency of the amino acids at \(L=3\). Between the RF and QDA models, there are two standard features: ACC445, representing the cross-covariance between the relative frequency of the amino acids at \(L=5\), and ACC523, representing the cross-covariance between the propensity of amino acids to occur in \(\beta\)-strands and their molecular size at \(L=3\). Finally, since both RF and XGBoost were used to derive models for immunogenicity prediction of proteins and peptides, we examined if there are any common attributes between the models derived from each algorithm, regardless of the feature importance technique used. For RF, the protein and peptide models assessed by the permutation feature importance technique shared one common feature: ACC234, representing the cross-covariance between the amino acid size and their relative frequency at \(L=4\). Additionally, the drop-column feature importance for the protein RF model and the permutation feature importance for the peptide RF model also shared one common feature: ACC341, representing the cross-covariance between the propensity of amino acids to occur in \(\alpha\)-helices and their relative frequency at \(L=1\). For XGBoost, the drop-column feature importance for the protein model and both the drop-column and permutation feature importance for the peptide model shared one common attribute, ACC441, which has already been discussed. Furthermore, the drop-column feature importance for both the protein and peptide XGBoost models shared another common feature: ACC254, representing the cross-covariance between the amino acid size and the propensity of amino acids to occur in \(\beta\)-strands at \(L=4\). While our feature importance analyses successfully identified the most influential descriptors, several important limitations must be acknowledged regarding their interpretation. First, the auto- and cross-covariance transformation inherently obscures direct biological interpretability, as the derived features represent complex correlations rather than discrete physicochemical properties. Second, while our methods reveal statistical associations between specific E-descriptor patterns and immunogenicity, they cannot establish causal relationships.