## 3 Feature Selection and Decision
### Hybrid Feature Decision  
This study proposes a hybrid feature selection algorithm that integrates the F-test, RNCA, and AIC to select valuable features for BP and CI estimations. Feature selection typically comprises two steps: calculating the weight for each feature and selecting the optimal subset as input features. Therefore, the F-test [38] was used to obtain a set of ranked features. Subsequently, the RNCA [39] was applied to select weighted feature vectors from among the original features. The AIC [40] was then used to determine the best feature subset. Finally, the AIC measured the quality of the selected features from the F-test and RNCA to determine the hybrid situation, as indicated in Algorithm 1. Feature selection involves selecting essential features that are more uniform, nonoverlapping, and effective in improving the performance of ML algorithms. As mentioned in the introduction, the best feature subset with high weights was obtained from the original feature set. Additionally, reducing the number of features by determining which features have higher weights makes ML algorithms easier to understand and explain. Feature Weighting Using the F-Test  
This study used the F-test to select meaningful features for BP estimation [38]. The F-test is a statistical test weighted by computing the variance ratio. In this study, the F-test based on a one-way ANOVA was used to calculate the between- and within-group variance ratios for each feature. A group represented the instances with the same response value. Higher weights indicated shorter intragroup distances and greater intergroup distances. Thus, features were ranked based on higher weights using an F-test based on a one-way ANOVA [38]. The null hypothesis was that the target values grouped by function in each F-test were drawn from populations with the same mean, as opposed to the alternative hypothesis that all population means were unequal:  
\[\mathcal{H}_{0}:\mu_{1}=\mu_{2}=...=\mu_{m},\quad\mathcal{H}_{1}:\mu_{1}\
eq \mu_{2}\
eq...\
eq\mu_{m} \tag{1}\]  
where \(m\) is the number of group and \(\mu_{m}\) denotes the mean for group \(m\). The overall mean was calculated as  
\[\mu=\frac{1}{n}\sum_{k=1}^{m}\mu_{k}n_{k},\quad(n=\sum_{k=1}^{m}n_{k}) \tag{2}\]  
where \(n_{k}\) is the number of the \(k\)th group. Hence, the mean of a real feature's samples was given by  
\[\bar{x}_{k}=\frac{1}{n}\sum_{j=1}^{n_{k}}x_{ik}, \tag{3}\] \begin{table}
\begin{tabular}{l l l} \hline \hline
**Features** & **Explanation** & **Ref.** \\ \hline
10: S1 & Area under the PPG pulse curve from the diastolic trough to & \\  & the point of max slope & [26; 28] \\
11: S2 & From the point of max slope to the systolic peak & [26; 28] \\
12: S3 & From the systolic peak to the inflection point closest to the diastolic peak & \\
13: S4 & From the inflection point to next pulse’s diastolic trough & [28] \\
14: Inflection point area ratio (IPAR) & Ratio of S4/(S1+S2+S3) & [26; 28] \\
15: PPG\({}_{k}\) & \((\mathrm{p_{m}-pd})/(\mathrm{p_{s}-pd})\) & [26] \\
16: dPPG height (H) & PPG\({}_{k}\) IS derivative characteristics & [14; 28] \\
17: dPPG width (W) & PPG\({}_{k}\) IS4 derivative characteristics & [14; 26] \\
18: dPPG weak height (PH) & PPG\({}_{k}\) IS2 nd derivative characteristics & [14; 26] \\
19: dDPG trough height (TH) & PPG\({}_{k}\) IS2 nd derivative characteristics & [14; 26] \\
20: dDPG width (W) & PPG\({}_{k}\) IS2 nd derivative characteristics & [14; 26] \\
21: dDPG height (H) & PPG\({}_{k}\) IS2 nd derivative characteristics & [14; 26] \\
22: MXAP & The pulse’s maximum amplitude & [30] \\
23: MIAP & The pulse’s minimum amplitude & [30] \\
24: MEU & The blood’s viscosity & [30] \\
25: FIR & The frequency of HR & [30] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of the features, part II, where \(\mathrm{p_{m}}\) denotes the area under the pulse divided by the pulse duration, \(\mathrm{p_{d}}\) is the minimum intensity of the PPG signal, and \(\mathrm{p_{s}}\) denotes the maximum intensity of the PPG signal.