## 3 Results
### Fixed State Error Correction  
Figure 14 shows the accuracy of the network classification results, as well as the F1 scores detected for S1 and S2 events of different state annotation methods, and it should be noted that the evaluations of the accuracy and F1 scores are different. LSTM and TCN were modeled and tested over 100 times, and a small part of the obvious deviation from the average result was deleted because of over-fitting during network training. The results shown in Figure 14 indicated that the variability was consistent between the results before and after correction, thereby demonstrating that the accuracy of feature classification greatly influenced the final results. Therefore, it would very useful to identify an algorithm with high accuracy. The testing results obtained by TCN and LSTM were almost the same with the LH-training testing set, but the error correction results produced by the TCN network with the manually labeled PN-training-a were better than the results yielded by LSTM. Therefore, similar classification results may yield different final results after applying the Viterbi algorithm. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Net**} & \multicolumn{4}{c}{**Accuracy**} \\ \cline{2-5}  & **PN-Training-a** & **LH-Training** & **Parameter Number** & **FLOPs** \\  & **Testing Set (\%)** & **Testing Set (\%)** & & \\ \hline TCN & 90.98 & 92.48 & 112k & 221k \\ LSTM & 91.26 & 93.13 & 515k & 387k \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of LSTM and TCN. Figure 13: Accuracy of TCN classification results with different kernel sizes and stack numbers. (**a**) kernel. (**b**) stack. According to the performance of the different error correction algorithms shown in Table 3, the results obtained by Viterbi (Poisson, \(\alpha=1\)) and Viterbi (Gaussian, \(\alpha=0.2\)) with TCN and LSTM were similar, and they were significantly better than the results produced with LMSA and Viterbi (Gaussian, \(\alpha=1\)), while Viterbi (Gaussian, \(\alpha=1\)) performed slightly better than LMSA. Based on the similar classification results, the final results showed that TCN performed better than LSTM with PN-training-a. LH-training can be approximately considered as a processed version of PN-training-a, so the results showed that TCN was more stable than LSTM with noise heart sounds. In future mobile applications, the collected heart sounds will be more similar to those in PN-training-a, so TCN is more suitable for future applications on portable devices than LSTM. Table 4 compares our best experimental results and the results obtained by several literatures of recent algorithms. It should be noted that many HSS algorithms use different data sets, and the numbers of heart sounds in different databases are all relatively small. Due to the variations in the heart sounds caused by noise interference and heart diseases, the results obtained by various algorithms will differ among databases with variable classification difficulty levels. In addition, the evaluation methods can be different, which will obviously greatly affect the final score, so comparisons of the results should be combined with an evaluation method. The final annotations given in previous studies [3, 8, 13] and those obtained using TCN + Viterbi (Poisson, \(\alpha=1\)) were corrected with the Viterbi algorithm, so the state labeled all matched with the order of S1-systolic-S2-diastolic, therefore the evaluations were all conducted with event-based approaches. Besides, [PERSON] et al. [15] proposed a new approach based on events for evaluation, but no error correction methods were mentioned, so we speculate that better results can be obtained if error correction is performed after classification. [PERSON] et al. [18] also reported results obtained without error correction, where the final annotation by the algorithm involved assigning the signal to three states comprising S1, S2, and not S1 or S2, and the evaluation method was the same as the classification accuracy assessment.