## 3 Results
### Impact of Processing Strategies  
In order to analyze the effect of the sample data-processing method used in this experiment, we used the dataset without processing and the dataset using only the variable-importance processing to train the learner. The training accuracy of the model was compared with the effect of the method used in this experiment. The training accuracy comparison results of the three groups of models are shown in Figure 8. And the comparison to other researches and summarized is shown in Table 8  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Training**} & \multicolumn{6}{c}{**Positive = 2.5**} \\ \cline{2-7}  & \(P_{\textbf{2.5-0}}\) & \(R_{\textbf{2.5-0}}\) & \(P_{\textbf{2.5-2}}\) & \(R_{\textbf{2.5-2}}\) & \(P_{\textbf{2.5-3}}\) & \(R_{\textbf{2.5-3}}\) \\ \hline
50\% & 90.00\% & 100.00\% & 94.74\% & 100.00\% & 100.00\% & 100.00\% \\
60\% & 90.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% \\
70\% & 91.67\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% \\
80\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% \\
90\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: Inter-class precision and recall of HY = 2.5 as positive.  
Figure 8: The training accuracy of the raw data, permutation-variable importance processing and persistent entropy.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Training**} & \multicolumn{6}{c}{**Positive = 3**} \\ \cline{2-7}  & \(P_{\textbf{3-0}}\) & \(R_{\textbf{3-0}}\) & \(P_{\textbf{3-2}}\) & \(R_{\textbf{3-2}}\) & \(P_{\textbf{3-2}}\) & \(R_{\textbf{3-2}}\) \\ \hline
50\% & 100.00\% & 100.00\% & 91.67\% & 100.00\% & 100.00\% & 100.00\% \\
60\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% \\
70\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% \\
80\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% \\
90\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% \\ \hline \hline \end{tabular}
\end{table}
Table 7: Inter-class precision and recall of HY = 3 as positive.  
From the comparison results, we can see that the training accuracy of the model trained by the combination of variable-importance processing and TDA persistent entropy was up to 99.23% (the training samples accounted for 90%). The training accuracy of the model trained with the dataset treated by the importance of variables did not increase with the increase of the proportion of training samples (96.86%, 80%; 96.52%, 90%), and maintained at this level. Without data processing, the training accuracy of the model trained by the learner appeared as a U-shaped curve from high to low and then to high; when the training set accounted for 50% to 90%, the training accuracy was 93.75%, 92.89%, 91.97%, 93.72%, and 96.57%, respectively. The reason for this is that SVM could well fit a small number of samples, while the features of the data without processing were not obvious, and the influence of irrelevant features was greater. As the number of samples increased, more complex information appeared, which reduced the training accuracy. When the number of samples increased further, the learner acquired more information, which made the training accuracy increase. In conclusion, the training effect of SVM in a small sample dataset was excellent, and the irrelevant features could be eliminated by variable-importance processing to avoid overfitting of the training model. Using topology analysis and persistent entropy training could further enhance the discrimination of samples and significantly improved the training accuracy.