# Early Ventricular Fibrillation Prediction Based on Topological Data Analysis of ECG Signal
## 3 Results
### Features Ranking  
In order to verify the characterization performance of the proposed TDA features, we applied five features selection methods (MI, chi-square tests, minimum redundancy maximum relevance (MRMR), out-of-bag predictor for RF, and ReliefF algorithm) to rank the three types of features. Among them, MI method uses MI values to measure the correlation between the features [35]. Chi-square tests rank features using the \(p\)-values of the statistics [36]. MRMR method minimizes the redundancy of the feature set and maximizes the relevance of the feature set to the response variable [37; 38]. Out-of-bag method measures the influence of the features on the prediction results [39; 40; 41]. The ReliefF algorithm finds the appropriate weight for each feature through the reward and penal  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\mathbf{\tau}\) & **5 s Split Frame** & **8 s Split Frame** & **10 s Split Frame** & **15 s Split Frame** \\ \hline
11 & 90.0\% RF & 86.7\% RF & 88.3\% DT & 83.3\% DT \\
12 & 91.7\% RF & 93.3\% RF & 88.3\% RF & 83.3\% RF \\ \hline \hline \end{tabular}
\end{table}
Table 4: VF prediction accuracy of superior classifiers.  
Figure 6: Probability density curve of the embedding dimension.  
mechanism [42; 43; 44]. Table 6 shows the predictor importance scores of each feature for each method.  
Since each method yielded a different range of predicted impact scores, all features were ranked in each method based on Table 6. For each feature, the average of its five ranking values in the different methods was calculated; the average ranking of each feature is shown in order in Figure 7.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Features** & **MI** & **Chi\(-\)Square** & **MRMR** & **Out-of-Bag** & **ReliefF** \\ \hline TDA0\_sum0 & \(-\)0.06973 & 8.52156 & 0.14073 & 0.35355 & 0.22132 \\ TDA1\_sum1 & \(-\)0.05626 & 9.05480 & 0.16236 & 0.38521 & 0.26416 \\ TDA2\_sum2 & \(-\)0.26306 & 1.10083 & 0.05174 & 0.06355 & \(-\)0.04202 \\ TDA0\_var0 & \(-\)0.02478 & 12.90666 & 0.36806 & 0.70518 & 0.58501 \\ TDA1\_var1 & \(-\)0.08660 & 4.96328 & 0.13049 & 0.29902 & 0.20516 \\ TDA2\_var2 & \(-\)0.05625 & 10.68233 & 0.26268 & 0.48215 & 0.26509 \\ TDA1\_mean1 & \(-\)0.03002 & 11.78756 & 0.29908 & 0.62190 & 0.40754 \\ TDA2\_mean2 & \(-\)0.12454 & 1.84986 & 0.12685 & 0.17107 & 0.12099 \\ \(MNN\) & \(-\)0.13324 & 1.77568 & 0.10477 & 0.14286 & \(-\)0.08333 \\ \(SDNN\) & \(-\)0.39715 & 0.18215 & 0.00018 & \(-\)0.14286 & \(-\)0.14500 \\ \(RMSSD\) & \(-\)0.83429 & 0.06164 & 3.49049 \(\times\) 10\({}^{-15}\) & \(-\)0.14286 & \(-\)0.15243 \\ \(NN50\) & \(-\)0.31335 & 0.76527 & 0.00076 & \(-\)0.10643 & \(-\)0.12677 \\ \(PNN50\) & \(-\)0.27056 & 1.06271 & 0.04106 & 0.00000 & \(-\)0.07877 \\ _kurtosis_ & \(-\)0.31891 & 0.39783 & 0.00071 & \(-\)0.14286 & \(-\)0.13620 \\ _skewness_ & \(-\)0.09189 & 2.35361 & 0.13049 & 0.24026 & 0.13275 \\ _CV_ & \(-\)0.27523 & 1.03846 & 0.02133 & \(-\)0.03349 & \(-\)0.09768 \\ \(\kappa\) & \(-\)0.13934 & 1.15556 & 0.05641 & 0.09654 & 0.07217 \\ \hline \hline \end{tabular} Where \(m\) is 6, \(\tau\) is 12, and split frame length is 5 s.  
\end{table}
Table 6: Predictor importance scores for five features selection methods.  
Figure 7: Average rank of each feature.  
From Figure 7, the TDA features appear, generally, in higher-ranking positions, indicating that the characterization performance of the proposed features is superior than that of the other two previous features.