## 6 Result  
### Dimensionality Reduction  
Principal component analysis (PCA) was conducted to find the proportion-of-variance (pov), explained curve, and scree plot which indicates the number of dimensions with the most variance to be selected. When considering the scree plot for the entire spectrum of the sample, it was observed that only half (50%) of the variance is explained by the component, as depicted in (Figure 4a). Moreover, when we analyzed the contribution of every feature to this component, we realized that every feature approximately contributes the same amount to it, as depicted in (Figure 4b). Therefore, it is too difficult to conclude any feature selection and data reduction based on these observations. As a matter of fact, for a model to be estimated accurately, it is practical to focus on feature reduction based on the principal component when some features are dominated by others in regard to the variance explained, which is not the case here. Nevertheless, after projecting the dataset on the plane defined by the two first principal components (the plane explained by the most variance), as depicted in Figure 5, it is clear that the samples cluster into two different groups. And, obviously, these groups correlate to the two different sources of data that are considered in this study. What we can infer from this is that the principal source of variance within the dataset is the origin of the samples. Such a link between the samples and the source of variance was expected since the data from MIMIC-II were acquired in different environments from different subjects with different health conditions and physiological characteristics. The extracted featureswould have been our main source of variance if a larger dataset had been utilized from larger patients. From Figure 5, the X-axis represents the projection on the PC1 axis in association with PC1. The axes demonstrate the principal component scores. First, we can see that samples from subject 1 and subject 2 are located closer to each other, which indicates that they all belong to the same species of subject. Secondly, it can be noticed that subject 2 has relatively lower PC1 scores [\(-0.5\), 0], whereas subject 2 has rather higher PC1 scores [0, 0.5]. Finally, we can see that features such as DT, ST, AI, AUC2, ddppgFH, ddppgPH, dppgH, AUC3, PIR, and AUC4 are in the same direction as PC1; consequently, they are positively correlated with PC1, which implies a positive association. When the subsets of each subject are analyzed separately into their own plane, we can note that subject 2 expressed more variation than subject 1 (Figure 6). This was expected because subject 2's PPG signal's amplitude varied more across the samples (Figure 1). Figure 4: (a) Scree plot of the percentage of total variance explained by each principal component. (b) Feature weights in the first principal component. Figure 5: Projection of all the data points onto the plane defined by the first two PCs and projection of features onto the same plane. Most of the features are positively correlated for each subject (Figure 6), which means they have relatively higher scores in PC1. When feature weight analysis was performed on the first principal component, it was observed that each feature explained similar variance among subsets; for example, features like the first and second derivative of PPG maximum intensity (dppgH, ddppgPH) are likely to explain the same amount of variance in the two subsets, but AUC2 explained different amounts of variance in subject 1 and subject 2. Analyzing the weight distribution on the first principal component of the subset (depicted in Figure 4b) allows us to grasp the similarity in variance explained by individual features across subjects. Notably, features DT, ddppgPH, and dppgH appear to explain a similar relative variance in the subsets.