## 5 Discussion  
In the discrete blood pressure models, the feature extraction models consistently outperform the deep learning models. For SBP, only the two larger feature-trained ANNs meet the 85% criterion. For DBP and MAP, all feature-trained ANNs and the binary decision tree meet the criterion. None of the deep learning models trained on the full waveform meet the criterion, although the ANNs for the DBP do come relatively close. It is worth examining the deep learning models' performance. The LSTM and CNN models have very low \(R^{2}\) values, and the CNN actually produces a constant value for the DBP and MAP. This shows these models are underfitting the data. The results produced by the ANNs on the full wave are similar to those achieved by [PERSON] et al. (2014), who, at best, achieved an MAE of 9.42 mmHg and 6.88 mmHg for SBP and DBP, respectively. No other performance metrics are given in the paper. [PERSON] (2014) achieved far lower MAEs; however, the study only includes 121 patients. In fairness, those discrete valued predictions made use of a ResNet-18 architecture. This was not implemented because it is not described how the 1D signal data was resized for the ResNet architecture (which is intended for 2D images of size 224 by 224) or whether the tens of layers in ResNet-18 were all rewritten for 1D signals. This being said, none of the four other deep learning approaches in this study achieved acceptable results, and the [PERSON] et al. 's models still had relatively low \(R^{2}\) values (approximately 0.3 to 0.4). [PERSON] and [PERSON] (2014) also achieved effective results with deep learning (low MAE and high \(R^{2}\)), using only 100 subjects. In both papers, it is possible that the models would not generalise well for larger sample sizes, though this remains to be tested. This does not mean that the deep learning approach is not of value. It greatly simplifies the signal processing by cutting out the feature extraction. It is possible that with more complex architectures (such as ResNet (2014), or U-Net (2014)) and/or more hyperparameter tuning the deep learning approach will yield better results. For the best performing models (the two-layered feature ANNs for DBP and MAP and the four-layered feature ANN for SBP), the standard deviation (SD) of error has also been calculated. The SBP's test error (MAE \(\pm\) SD) is 5.26 \(\pm\) 6.53 mmHg. For DBP it is  
Figure 5: Generated ABP Waveforms using neural network models. \begin{table}
\begin{tabular}{c c c c} \hline \hline \# & **Structure** & **Regression** & \(r\) \\ \hline
1 & 3 \(\times\) fc(1024) & Pearson & 0.864 \\
2 & 2 \(\times\) bilstm(1024) & Standard & 0.801 \\
3 & 2 \(\times\) bilstm(1024) & Standard & 0.797 \\
4 & 2 \(\times\) bilstm(1024) & Pearson & 0.802 \\
5 & 2 \(\times\) lstm(1024) & Standard & 0.781 \\
6 & 2 \(\times\) lstm(1024) & Pearson & 0.818 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of various neural network architectures for waveform regression. Row 1 corresponds to the final model chosen. 2.96 \(\pm\) 3.31 mmHg and for MAP the test error is 3.27 \(\pm\) 3.55 mmHg. All meet the minimum criterion in [15]. Both LSTM and fully connected ANN networks show potential for the estimation of the wave shape, especially when modified to maximise on this shape specifically and not the absolute values. However, the simpler ANN network is both more computationally efficient and yields a higher correlation. The average waveform Pearson correlation of 0.864 implies that the waveform output is strongly correlated to the reference waveforms. In the literature survey, the maximum [PERSON]'s correlation was achieved by [PERSON] and [PERSON] [12], using a U-net architecture that yielded a correlation of 0.993. However, there are two key differences. Firstly, the study by [PERSON] and [PERSON] used only 100 subjects, whereas this study used data from 1669 patients. Secondly, the PPG and ABP signals were phase-matched before training the models.