## 3 Methodology
### Confusion Matrix  
A confusion matrix table is frequently used to assess whether a classification model is working well. It displays the proportion of precise and imprecise predictions generated by the model in contrast to the actual results. It is commonly depicted as a square matrix with rows and columns corresponding to the predicted and actual classes, respectively. The confusion matrix is used to evaluate a model's performance, notably its accuracy, precision, recall, and F1 score (Figure 7). The accuracy of the model is determined by dividing the total number of predictions by the sum of true positives and true negatives. Precision is determined by dividing the number of true positives by the total number of positive predictions, whereas recall is determined by dividing the number of true positives by the total number of positive predictions. The harmonic mean of recall and precision is the F1 score. The four outcomes of a binary classification model are:  
* True positive (_TP_): The model accurately predicted the positive class. * False positive (_FP_): The model predicts that the class would be positive, but the actual class was negative. * True negative (_TN_): The model predicted the negative class in the appropriate order. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **Accuracy** & **MAE** & **MSE** \\ \hline FFNN & 98.0275 & 0.0262 & 0.0318 \\ \hline FFNN-PSO & 98.615 & 0.0193 & 0.0253 \\ \hline AEC & 52.8\% & 37.3 & 7.48 \(\times\) 10\({}^{3}\) \\ \hline (1D) Convolutional Neural Network (CNN) [16] & 92.71\% & - & - \\ \hline Random Forest [16] & 89.10\% & - & - \\ \hline ReLU CNN [17] & 95.9\% & - & - \\ \hline GRU [18] & 96\% & - & - \\ \hline LSTM [18] & 90\% & - & - \\ \hline Bi-LSTM [18] & 91\% & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The final average results of the performance of the proposed models compared with similar work. Figure 7: Confusion matrix. * False negative (_FN_): The model indicated that the class would be negative, but it was actually positive. \[Accuracy=\left( \begin{array}{c}\dfrac{TP+TN}{TP+TN+FP+FN}\end{array} \right)\] (1) \[Sensitivity=Recall=\left( \begin{array}{c}\dfrac{TP}{TP+FN}\end{array} \right)\] (2) \[Positive\;Predictive\;Value=Precision=\left( \begin{array}{c}\dfrac{TP}{TP+FP} \end{array} \right)\] (3) \[F1\;score=2\times\left( \begin{array}{c}\dfrac{Precision\times Recall}{ Precision+Recall}\end{array} \right)\] (4)  
The dataset's confusion matrix of human falling detection is evaluated by the findings with four labels on the actual and predicted labels, which have an accuracy of 98.615% and have been processed using the FFNN-PSO algorithm. This shows that falling forward using knees has the highest number of predictions (16,008), while falling forward using hands receives the lowest prediction (eight at the same time). Precision and recall are important for evaluating system performance. Precision measures the system's ability to correctly identify positive results, while recall measures the system's ability to correctly identify all positive results. The values of precision and recall depend on the number of true positives, false positives, and false negatives. The F1 Score depends on the value of precision and recall and is used as a measure of a system's accuracy. Regarding matrix results, indicating that the FFNN_PSO model had achieved precise performance for activities with a precision of 98.9%, recall of 95.2%, and F1 score of 97.1%, the prediction error is about 0.0224. The value of precision and recall is used as a measure of a system's accuracy. For BSC falling, 15,925 actual samples were correctly classified as true positive (TP), while only eight samples were incorrectly classified as false positive (FP). For FLR falling, 16,008 samples were correctly classified as (TP), and 388 samples were incorrectly classified as FKL or SDL (FP).