## 2 Materials and Methods
### Implementation of the EC-Nomenclature-Based G-S-M Model  
The first component (G component) of the proposed G-S-M plays a crucial role in creating sub-datasets for each enzyme commission (EC) term. This component focuses on the annotation of several enzymes with specific EC terms and then extracting a sub-dataset for each EC term from the relative enzyme abundance dataset. In essence, these sub-datasets are tailored to include abundance values solely for the enzymes associated with a particular EC term, along with the class labels of the samples, whether positive or negative. It is important to highlight that, while each sub-dataset contains an equal number of samples, the number of features varies based on the number of enzymes annotated with the specific EC term. This process is further elucidated in Figure 2, which visually represents a flowchart for generating sub-datasets based on the enzymes linked to a specific EC term. Each sub-dataset is uniquely named as \"ECterm(i)_sub_dataset\", where 'i' starts from 1 and increments up to k, the total number of EC terms considered.  
The G component operates with two key tables, as follows: the EC terms table, where each EC term is connected to a set of enzymes, and the relative enzyme abundance dataset. Figures 2 and 3 depict the creation of four distinct sub-datasets, each corresponding to a particular EC term based on this process. Following the G component, component S steps in, denoted as \"S\" in the latter part of Figure 2, to conduct the scoring phase using the generated sub-datasets. Component S leverages machine learning algorithms, specifically  
Figure 2: The proposed EC-nomenclature-based G-S-M workflow for analyzing enzyme abundance values obtained from disease-associated metagenomics relative enzyme abundance datasets.  
RF in this study. It implements an internal Monte Carlo Cross-Validation (MCCV) process, which is repeated r times, as indicated in Figure 3 (represented with a yellow triangle on the top right). This scoring mechanism assesses the classification performance of each EC term, indicating the accuracy of classification solely based on the enzyme abundance values associated with that specific EC term. The classification accuracy is averaged across r iterations of MCCV to derive a mean accuracy value, which serves as the final importance score for the respective EC term. Subsequently, S ranks all EC terms based on their scores, with the top-scoring EC terms moving to the next phase for model training.  
Furthermore, the M component trains the classifier and constructs the model, following a cumulative approach, as illustrated in Figure 3 (represented with a yellow triangle on the bottom right). This component utilizes the enzyme abundance values linked to the top-scoring EC terms for model training. The iterative process starts with building an RF model using enzymes annotated with the highest scoring EC term and continues by progressively incorporating enzymes associated with subsequent high-scoring EC terms. This cumulative strategy enables the calculation of the model's overall performance, facilitating the comparison of performance results across different feature sets, ranging from the highest scoring EC term to the top 10 highest scoring EC terms. By evaluating the model's performance over various feature sets, one can identify the optimal combination of enzymes annotated with the top-scoring EC terms. The M component provides insights into the average performance metrics of classification using enzymes tied to the top 10 highest scoring EC terms, averaged over a 10-fold MCCV, offering a comprehensive evaluation of the model's efficacy. The output of the M component includes the performance  
Figure 3: Detailed description of the grouping, scoring, and modeling components in the proposed EC-nomenclature-based G-S-M approach.  
measurements (accuracy, sensitivity, specificity, and AUC metrics), ranked EC groups, and ranked features (enzymes).