# MEMS and IoT in HAR: Effective Monitoring for the Health of Older People
## 5 Data Analysis
### Prediction
\begin{table}
\begin{tabular}{c c} \hline \hline
**Hyperparameters** & **Function** \\ \hline Estimators & This specifies the number of decision trees in the forest \\ \hline max\_features & This indicates the number of features to consider when splitting each node as a fixed value or a fraction of the total features. \\ \hline max\_depth & This limits the depth of each tree to avoid overfitting. \\ \hline min\_samples\_leaf & This defines the minimum number of samples needed to form a leaf, with higher values reducing overfitting. \\ \hline min\_samples\_split & This specifies the minimum number of samples required to split a node, also helping to control overfitting. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Hyperparameters of Random Forest. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Precision** & **Recall** & **F1-Score** & **Accuracy** \\ \hline Arm Cir. Mov. & 0.998875 & 0.998885 & 0.998857 & 0.998885 \\ \hline Walking & 0.998765 & 0.998786 & 0.998783 & 0.998885 \\ \hline Grasping & 0.998675 & 0.998775 & 0.998763 & 0.998576 \\ \hline Leg Flexion & 0.998657 & 0.998665 & 0.998648 & 0.998665 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Evaluation metrics. Figure 16 illustrates the ROC curve representing the classification model's performance. The False Positive Rate (FPR) is shown on the \(y\)-axis, and the True Positive Rate (TPR) is displayed on the \(x\)-axis. The area under the curve represents the AUC (Area Under the Curve). This value indicates how well the model can differentiate between the various asset classes examined. A value of 1 means that the model can accurately identify positive and negative classes without errors. To validate the performance, the model was compared with another neural network, the self-normalizing neural network (SNN). This type of neural network is designed to keep the activation of its neurons within a desired range without requiring external normalization techniques, such as batch normalization. Each layer is normalized and serves as input to the next layer. SNNs utilize self-normalizing neural activations that automatically converge toward a mean of zero and a unit variance. This is achieved through the SELU (Scaled Exponential Linear Unit) activation function. The SELU function accelerates convergence during training, allowing it to learn faster and more effectively than other activation functions without additional processing. The SELU can be expressed mathematically as follows:  
\[ \begin{array}{l}\text{f(x)}=\lambda\times\text{x}\hskip 56.905512 pt\text{if x >0}\\ \text{f(x)}=\lambda\times\alpha(\text{ex}-1)\hskip 56.905512 pt\text{if x \leq 0}\end{array}  \tag{2}\]  
Graphically, it can be represented as in Figure 17.  
The SELU (Scaled Exponential Linear Unit) function is continuous and differentiable throughout its entire domain, including the origin. This property ensures there are no jumps or discontinuities in the curve, which is beneficial for optimization during the training of neural networks. In the positive region (X > 0), the SELU function behaves linearly. This means the output increases proportionally with the input. The scale parameter, approximately equal to 1.0507, determines the slope of the curve in this region. In the negative region (X < 0), the SELU function applies an exponential transformation. This transformation keeps the output close to zero, but not exactly zero, which helps mitigate the \"dying ReLU\" problem, where neurons stop updating during training. The alpha parameter, approximately 1.67326, influences the curve in this region. Figure 16: ROC curve. The convergence property of SELU networks allows them to trend towards a mean of zero with unit variance, enabling the training of deep networks with many layers and making the learning process highly robust. The metrics obtained were as follows (see Table 4). The ROC curve was also derived for the SNN network (Figure 18).