## 3 Materials and Methods
### Data Analysis  
In this study, we employed several key metrics to assess the performance of our deep learning model in predicting fall risk. These metrics are commonly used in classification tasks, especially in medical and biomechanical studies, to evaluate the balance between correctly and incorrectly classified instances. Below are the operational definitions of each metric:  
* Accuracy: Accuracy is the ratio of correctly predicted observations to the total observations. It is a measure of how well the model predicts both fallers and non-fallers. The formula for accuracy is \[Accuracy=\frac{TP+TN}{TP+TN+FP+FN}\] where \(TP\) represents true positives, \(TN\) true negatives, \(FP\) false positives, and \(FN\) false negatives [82].
* Precision: Also known as positive predictive value, precision is the ratio of correctly predicted fallers (true positives) to all the instances classified as fallers (true positives and false positives). Precision is crucial when the cost of false positives is high [83]: \[Precision=\frac{TP}{TP+FP}\]
* Recall (Sensitivity): Recall, or sensitivity, measures the model's ability to correctly identify all the fallers (true positives). A high recall indicates that the model successfully detects most of the actual fallers [84]: \[Recall=\frac{TP}{TP+FN}\]
* Specificity: Specificity, or true negative rate, refers to the ability of the model to correctly identify non-fallers, i.e., the proportion of true negatives among all the actual non-fallers [84]: \[Specificity=\frac{TN}{TN+FP}\]* \(F1\) Score: The \(F1\) score is the harmonic mean of precision and recall, providing a single metric that balances both: \[F1=2\times\frac{\textit{Precision}\times\textit{Recall}}{\textit{Precision}+ \textit{Recall}}\] This metric is especially useful when dealing with imbalanced datasets, as it accounts for both false positives and false negatives [85].
* Balanced Accuracy: Balanced accuracy is the average of recall and specificity. It is used to handle imbalanced datasets by considering both fallers and non-fallers equally [86]: \[\textit{Balanced}\textit{Accuracy}=\frac{\textit{Recall}+\textit{ Specificity}}{2}\]  
Operational Definitions of Performance Thresholds  
The classification of model performance was defined based on specific metric thresholds that indicate varying levels of effectiveness in predicting fall risk. These thresholds were categorized as follows:  
Low: A metric value below 70% was considered as low, indicating that the model's performed is suboptimal, with significant room for improvement in terms of classification or prediction accuracy. This suggests that the model may have high misclassification rates, failing to correctly identify a substantial number of cases [83].  
Moderate: Metric values between 70% and 85% were classified as moderate, meaning the model performed satisfactorily, but still risked missing a significant portion of true positives or introducing false positives. Although the model functions reasonably well, there were areas where improvements could be made, especially in increasing sensitivity or specificity [84].  
High: Metric values above 85% were defined as high, reflecting robust model performance with strong precision and recall. This level of accuracy indicates that the model was reliable in predicting outcomes, reducing both false positives and false negatives, and capturing complex patterns effectively [86].  
These thresholds were aligned with common practices in machine learning, where higher classification performance was generally marked by values close to 1 (or 100%) across multiple metrics, while lower performance was represented by values closer to 0. This scale provided a standardized way to assess the predictive ability of models and allows for a consistent comparison across different studies [82].