## 3 Discussion
### Models  
The serum metabolome differences between PASI classifications were initially assessed with PCA plots. PCA clusters patients or samples by grouping them based on their similarities, correlations and covariances with each other. However, PCAs in Figures 2 and 3 do not demonstrate meaningful and visible separation between PASI classes based on metabolite features gathered in this study. Considering that the existing literature has shown metabolome differences between PsA disease activity, the lack of separation suggests that PASI scores may not reflect subclinical metabolome differences between PsA patients of varying disease activity. On the other hand, in Figures 3 and 4, ML models built with select features were able to determine PASI disease activity classes with good predictability. This is likely due to PCA and ML models being designed for different functions. PCA models are generally designed as a dimensionality reduction method wherein features or metabolites in the samples are linearly combined into new variables called 'principal components' based on their covariance [20]. This approach is good for visualizing an otherwise complex dataset, but original variables (features) may lose meaning because of their transformation into derived variables (principal components) [20]. However, the ML models selected in this study are generally applied as methods of classification to identify the features most important for identifying differences in the sample groups (i.e., classes) [21]. Furthermore, the features selected for the models were selected based on how informative these features are for predicting class labels, and non-informative features are removed [21]. Using the  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Moderate vs. High** & **Low vs. Moderate** & **Low vs. High** & **Tentative Identification** \\
**(_m/z_)** & **(_m/z_)** & **(_m/z_)** & **Tentative Identification** \\ \hline
736.2599 & & 736.2599 & N/A \\
215.1279 & & 215.1279 & Medium chain fatty acids \\
680.3549 & & 680.3549 & N/A \\
496.3397 & & 496.3397 & Phospholipid, Acylcarnitine \\
159.1168 & & 159.1168 & Exposure—Benzene and derivatives \\
544.3373 & & 544.3373 & Lysophosphatidylcholine \\
688.3047 & & 688.3047 & N/A \\
116.0708 & & 116.0708 & Proline; Exposome-related Metabolites \\ \hline
415.2536 & & & Exposure—Peptides \\
769.4224 & 769.4224 & & Oxidized phospholipid \\
646.2575 & & & Exposure—Drug for increasing blood glucose concentration \\ \hline  & 668.5443 & 668.5443 & DAGs \\ \hline
549.1857 & 549.1857 & 549.1857 & Exposome—Neoacrimarine I/F \\ \hline \hline \end{tabular} N/A: No tentative identification available for this feature.  
\end{table}
Table 6: Tentative identifications of overlapping features between machine learning model groups.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \(m/z\) & **Retention Time** & **Adduct** & **Monoisotopic Mass** & **AUC** & **Tentative ID** \\ \hline
667.1419 & 11.98 & [M \(-\) H]\({}^{-}\) & 668.1506 & 0.63 & Etposide Phosphate; 1 other hit \\ \hline
448.3073 & 8.18 & [M \(-\) H]\({}^{-}\) & 449.3141 & 0.63 & Glycohydodeoxycholic acid; 7 other hits \\ \hline
388.1559 & 8.00 & [M \(+\) Cl]\({}^{-}\) & 353.1852 & 0.63 & Epiprorim \\ \hline
203.08299 & 3.58 & [M \(-\) H]\({}^{-}\) & 204.0899 & 0.63 & L-Tryptophan; 13 other hits \\ \hline \hline \end{tabular}
\end{table}
Table 5: _Cont._AUC to measure the performance of these classification models, it is concluded that the Naive Bayes (with 40 features), LogRegL (with 80 features), and SVM (with 10 features) model in Figure 3 has the best performance when predicting low vs. high, moderate vs. high, and low vs. moderate disease activity, respectively, in positive mode. However, only the SVM 10-feature model was able to exceed the minimum standard for acceptable performance, with an of AUC \(>\) 0.7, and only when predicting low and moderate skin disease activity (Figure 4C). Overall, there are metabolome differences between PsA patients of varying skin disease severity.