## 3 Background
### Binary Harris Hawks Optimizer (BHHO)
Unlike RF, ETR does not use bootstrapping and selects both features and split points randomly for each tree, creating diverse and simplified ensembles. While this increases speed and reduces complexity, it may result in slightly lower accuracy for capturing complex patterns compared to methods like LightGBM [50]. #### 4.3.3 Light Gradient Boosting Machine (LightGBM)

The LightGBM, created by Microsoft, is an advanced gradient boosting algorithm designed for scalability and efficiency. Leveraging Gradient-based One-Side Sampling (GOSS) to prioritize high-gradient samples and Exclusive Feature Bundling (EFB) to compress features, LightGBM achieves fast training and low memory usage. It is particularly suited for large datasets and high-dimensional problems but requires careful hyperparameter tuning. Although it offers excellent predictive accuracy, its complexity can pose challenges for interpretability [54; 51]. ### Algorithm Performance

The performance of the regression models was evaluated using three well-established metrics: Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Clarke Error Grid (CEG) analysis. These metrics were chosen for their ability to provide quantitative and clinically meaningful insights into the accuracy and reliability of BGL predictions. Their widespread use in ML studies ensures comparability with prior research and clinical applications [4, 5, 6, 7, 8, 9, 10, 11, 12]. MAE, as shown in Equation (19), quantifies the average absolute difference between predicted and actual values, offering an interpretable measure of overall prediction accuracy [10]. RMSE, represented in Equation (20), measures the standard deviation of prediction errors, providing insights into the magnitude of both small and large deviations, with greater sensitivity to outliers [10]. The CEG provides a clinically relevant evaluation by categorizing predictions into five zones (A to E) based on their potential impact on treatment decisions. Predictions in Zones A and B are considered accurate or acceptable, while those in Zones C, D, and E represent errors of increasing severity, with Zones D and E posing significant risks due to potential misclassification of hyperglycemia and hypoglycemia [55, 56]. \[\text{MAE}=\sqrt{\frac{\sum_{1}^{n}\left|yi-\hat{y}i\right|}{n}} \tag{19}\]

\[\text{RMSE}=\sqrt{\frac{1}{n}{\sum_{i=1}^{n}\left(\hat{y}i-yi\right)^{2}}} \tag{20}\]

where \(n\) is the number of samples, \(\hat{y}i\) represents the predicted value, and \(yi\) is the actual value. The dataset was split into training and testing subsets, with 80% of the samples used to train the regression models and the remaining 20% for testing. This splitting also made it possible to test the model on unseen data and therefore gave a fair estimation of the accuracy of the model in making its predictions. The results of the regression models and feature selection algorithms are detailed in Section 5, \"Results and Discussion\". ## 5 Experimental Results and Discussion

This section presents the experimental results obtained using the proposed non-invasive BGL estimation methodology. The analysis includes the outcomes of the preprocessing, feature extraction, and feature selection phases, followed by regression model performance. The results are compared with existing methodologies to show how the proposed method is better than the existing one. Every experiment was performed in Google Colab [57] using the Python programming language [58]; the platform availed a 12.7 GB memory and Intel Xeon 4 th Gen (Sapphire Rapids) processor. ### Results of Data Preprocessing Stage

The preprocessing stage was vital to enhance the signal quality of the PPG data. The dataset used, as described in Section 4.1.1, underwent preprocessing to remove noise and artifacts, as detailed in Section 4.1.2. The application of a third-order Butterworth filter with a bandpass of 0.5-8 Hz effectively eliminated baseline wander and high-frequency noise while retaining the physiological components essential for identifying systolic peaks.