## 2 Materials and Methods
### Our Proposed Method: EC-Nomenclature-Based G-S-M Approach  
The main idea of the G-S-M technique is to evaluate a group or groups of features rather than assessing individual features. Biological knowledge is used as a function applied to the feature space to create sets of groups, where each of the groups is a set of features (i.e., enzymes, genes). Figure 2 illustrates the main workflow of the proposed EC-nomenclature-based G-S-M approach. It involves three main components, i.e., the G Component, S Component, and M component. While the G component generates sub-datasets for each EC term group and the S Component scores the EC terms, the M Component trains the classifier using different classifiers, such as Random Forest (RF) and XGBoost, to build the model.  
The general G-S-M technique was developed by [PERSON] et al. [32] and was embedded in different computational tools, including the following: maTE [32], which uses microRNA target gene information for grouping genes; miRModuleNet [33], which analyzes mRNA and miRNA expression datasets concurrently to detect feature sets; CogNet [34] and PriPath [35], which use KEGG pathway information for gene grouping; miRdisNET [36], which uses miRNA target gene information to assign genes into groups; and GeNetOntology [37], which uses gene ontology (GO) terms to find disease-related gene ontology groups. AMP-G-S-M is another G-S-M-based approach used for the prediction of antimicrobial peptides [38]. The main idea and most of the relevant tools are reviewed in [39].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Country** & **\# of Controls** & **\# of CRC Patient** & **Total** \\ \hline Austria (AUT) & 61 & 46 & 107 \\ China (CHN) & 53 & 75 & 128 \\ Germany (DEU) & 65 & 60 & 125 \\ France (FRA) & 61 & 53 & 114 \\ Indian (IND) & 30 & 30 & 60 \\ Italy (ITA) & 49 & 57 & 106 \\ Japan (JP)/(JPN) & 291 & 227 & 518 \\ United State of America (USA) & 52 & 52 & 104 \\ Total & 662 & 600 & 1262 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Description of the CRC-associated metagenomic datasets collected from eight different countries.  
The main purpose of the proposed EC-nomenclature-based G-S-M method is to identify the most significant enzyme groups and enzyme terms (as scored in the S Component) to be used for training the classifier (realized in the M component) (Figure 2). In order to evaluate a set of features, for each EC term, a sub-dataset is created by only including the abundance values of the enzymes that are associated with that particular EC term (represented with the orange box). The enzyme abundance values of samples are represented by the C matrix (represented with the green box), which is divided into Ctrain and Ctest matrices. While Ctrain has been utilized for scoring the EC terms and training the classifier, Ctest has been used to test and report the final performance. The M component (represented with the yellow box) trains a classifier using the enzyme abundance values that are annotated with the top-scoring EC terms. Finally, the G-S-M model provides performance metrics, ranked groups, and ranked features as outputs. The G-S-M KNIME workflow is available publicly at: [[https://github.com/malikyousef/The-G-S-M-Grouping-Scoring-Modeling-Approach](https://github.com/malikyousef/The-G-S-M-Grouping-Scoring-Modeling-Approach)]([https://github.com/malikyousef/The-G-S-M-Grouping-Scoring-Modeling-Approach](https://github.com/malikyousef/The-G-S-M-Grouping-Scoring-Modeling-Approach)) (Accessed on 7 March 2023)