## 2 Materials and Methods
### Machine Learning Modeling Processes and Algorithms Evaluation  
The aim of this study was to obtain the best machine learning classifier and to find the most important morphological features for the detection of CAD. Moreover, to evaluate the quality of the selected morphological features for the detection of CAD, several commonly used classifier algorithms were applied for classification, namely LR, DT, LDA, k-NN, ANN, and SVM, respectively. In this study, the classification performances of the SVM model for three different kernel functions (namely linear, polynomial, and radial basis function (RBF)) were first studied to find the best kernel function for the detection of CAD. We named these three sub-algorithms as linear-SVM, polynomial-SVM, and RBF-SVM, respectively. Moreover, the accuracies among the best sub-algorithm of SVM and the other machine learning algorithms were further compared to assess the capability of all algorithms we used. This aim was to select the best machine learning algorithm for the following up researches. To find the most important features for the detection of CAD, we then applied the selected best algorithm to evaluate the classification performance of the specific feature(s) or their combinations. The process flow diagram of our proposed machine learning approach was shown in Figure 2. The main steps of the proposed approach were summarized below. _Step 1._ Collecting the original morphological features;  
In this study, we totally collected six original morphological features (\(\alpha\), \(n\), \(\frac{D_{1}^{3}}{D_{m}^{3}}\), \(\frac{D_{1}^{3}}{D_{m}^{3}}\), \(\frac{D_{1}^{3}}{D_{1}^{3}}\), and _AER_). These morphological features were selected since they had been shown highly correlating with CAD. _Step 2._ Dividing all the features into four equal groups;  
The morphological feature datasets for both CAD subjects and non-CAD subjects were randomly divided into four equal-sized subsets. The subsets of the non-CAD subjects were designated as \(A1\), \(A2\), \(A3\), and \(A4\); while the subsets of the CAD subjects were designated as \(B1\), \(B2\), \(B3\), and \(B4\) (Figure 2). This part was aimed to prepare for studying the effect of data sampling on the classification performance of the machine learning model. _Step 3._ Preprocessing of the original morphological features;  
To meet the requirement of the data format of the classifier algorithms, the original morphometric data were preprocessed. The preprocessing formula was described as follows:  
\[y=2\frac{x-x_{min}}{x_{max}-x_{min}}-1 \tag{1}\] \begin{table}
\begin{tabular}{l l} \hline \hline
**Features** & **Definitions** \\ \hline \(D_{m}\) & Diameter of mother vessel. \\ \(D_{l}\) & Diameter of larger daughter vessel. \\ \(D_{s}\) & Diameter of smaller daughter vessel. \\ \(\alpha\) & Bifurcation angle between larger and smaller \\ \(n\) & The exponent of vessel diameter: \(D_{m}^{n}=D_{l}^{n}+D_{s}^{n}\). \\ \(\frac{D_{s}^{3}}{D_{m}^{3}}\) & Ratio of diameters between smaller daughter and \\ \(\frac{D_{s}^{3}}{D_{m}^{3}}\) & mother vessels. \\ \(\frac{D_{s}^{3}}{D_{m}^{3}}\) & Ratio of diameters between larger daughter and \\ \(\frac{D_{s}^{3}}{D_{m}^{3}}\) & Ratio of diameters between smaller and larger \\ \(\frac{AER}{D_{s}^{3}}\) & daughter vessels. \\ _AER_ & Area expansion ratio: \(AER=\frac{D_{l}^{2}+D_{s}^{2}}{D_{m}^{2}}\). \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The definitions of the coronary morphological features. where \(x_{max}\) and \(x_{min}\) were the maximum and minimum values of each morphological feature, respectively. After data preprocessing, the values of original morphometric data were normalized to values ranging from \(-1\) to \(1\). _Step 4._ Choosing a machine learning model, training the selected model, and parameter tuning;  
Different classification algorithms (LR, DT, LDA, k-NN, ANN, linear-SVM, polynomial-SVM, and RBF-SVM) were applied for training under the use of same morphological features (75% of data for training, the remaining for testing).