## 2 Materials and Methods
### Performance Assessment  
After implementing SMOTE, the number of samples in \(S_{FFDC}\) was extended from 237 to 413, and from 186 to 370 in \(S_{OFDC}\), as shown in Table 2. The extended sample set is uniformly denoted as \(S\)S. In this study, we chose macro average arithmetic (MavA), macro average geometric (MavG), and mean F-measure (MFM) as the criteria to evaluate the classification performance [32]. These criteria have been widely used in multi-class imbalance datasets [33; 34; 35]. The confusion matrix for binary classification problems is shown in Table 3.  
The confusion matrix represents the results of correctly and incorrectly categorized samples. Here, the positive rate responds to the minority class and the negative to the  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Experiments** & **IA** & **MIA** & **AIS** & **Benign** \\ \hline \multirow{4}{*}{FFDC} & Before & Training set & 143 & 19 & 19 & 16 \\  & augmentation & Test set & 10 & 10 & 10 & 10 \\ \cline{2-6}  & After & Training set & 143 & 95 & 95 & 80 \\  & augmentation & Test set & 10 & 10 & 10 & 10 \\ \hline \multirow{4}{*}{OFDC} & Before & Training set & 100 & 14 & 14 & 18 \\  & augmentation & Test set & 10 & 10 & 10 & 10 \\ \cline{1-1} \cline{2-6}  & After & Training set & 100 & 70 & 70 & 90 \\ \cline{1-1}  & augmentation & Test set & 10 & 10 & 10 & 10 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The data distribution of augmentation anterior posterior.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**Predicted Class**} \\ \cline{2-4}  & & **Positive** & **Negative** \\ \hline \multirow{2}{*}{True class} & Positive & True positive (TP) & False negative (FN) \\  & Negative & False positive (FP) & True negative (TN) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Confusion matrix for the binary classification problems.  
majority class. In the binary scenario, several common assessment metrics can be derived from the confusion matrix, as shown in Table 4.  
The MavA comprehensively considers the classification results, and each class is assigned the same weight. It calculates the accuracy of each class independently, and then computes their mean to obtain the assessment result. Therefore, the MavA is considered the arithmetic mean of the individual accuracy of each class. MavG is defined as the geometric average of the accuracy for each class. MavA and MavG are formulated as  
\[\text{MAvA}=(\sum_{i=1}^{4}\text{TPR}_{i})/4 \tag{8}\]  
\[\text{MAvG}=(\prod_{i=1}^{4}\text{TPR}_{i})^{1/4} \tag{9}\]  
where \(\text{TPR}_{i}\) represents the accuracy rate for the class \(i\), \(i\) = 1, 2, 3, and 4.  
F-measure assigns the same importance degree to recall and precision. It is shown as follows:  
\[\text{F}-\text{measure}=2\times\text{recall}\times\text{precision}/(\text{ recall}+\text{precision}) \tag{10}\]  
The F-measure for two-class classification assessment can be extended to deal with multi-class assessment problems. In this paper, MFM was employed to evaluate the four-category task, defined as follows:  
\[\text{MFM}=(\sum_{i=1}^{4}\text{F}-\text{measure}_{i})/4 \tag{11}\]  
where \(i\) is the index of the class.  
Alternatively, we computed the area under the receiver operating characteristic (ROC) curve, which is also denoted by AUC. In order to extend ROC curve to multi-class classification, the output is binarized. The ROC curve can be drawn by calculating metrics for each label in a one-vs.-all manner and by finding their unweighted mean (macro-averaging). Figure 4 shows the schematic diagram of the FFDC method.