## 3 Results
### Fall Risk Assessment System  
Based on the results of Section 3.1, information is collected from the 86 subjects who met the exclusion criteria and had their Tinetti test results. To add to the database, the videos are divided into 5 s windows, segmenting the signals as shown in Figure 6. In this way, samples with 5 to 9 steps are available, which is sufficient for calculating the indicators proposed in Section 2.6. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Score** & **Frequency** & **Percentage** \\ \hline
19 & 2 & 2.3\% \\ \hline
20 & 2 & 2.3\% \\ \hline
21 & 2 & 2.3\% \\ \hline
23 & 3 & 3.5\% \\ \hline
24 & 6 & 7.0\% \\ \hline
25 & 10 & 11.6\% \\ \hline
26 & 18 & 20.9\% \\ \hline
27 & 22 & 25.6\% \\ \hline
28 & 20 & 23.3\% \\ \hline
29 & 1 & 1.2\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Frequencies of the Tinetti Scale scores. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Main Features** & **Group** & **Mean** & **Standard Deviation** \\ \hline \multirow{3}{*}{Cadence (_steps per minute_)} & No risk & 97.01 & 24.00 \\ \cline{2-5}  & At risk & 99.81 & 41.20 \\ \hline \multirow{3}{*}{Period (s)} & No risk & 1.29 & 0.30 \\ \cline{2-5}  & At risk & 1.44 & 0.70 \\ \hline \multirow{3}{*}{Stride (cm)} & No risk & 71.29 & 24.30 \\ \cline{2-5}  & At risk & 64.53 & 43.10 \\ \hline \multirow{3}{*}{Velocity (m/s)} & No risk & 58.54 & 20.60 \\ \cline{2-5}  & At risk & 57.09 & 55.50 \\ \hline \multirow{3}{*}{Max ROM (\({}^{\circ}\))} & No risk & 48.86 & 9.80 \\ \cline{2-5}  & At risk & 45.99 & 12.70 \\ \hline \multirow{3}{*}{Min ROM (\({}^{\circ}\))} & No risk & 3.95 & 3.50 \\ \cline{2-5}  & At risk & 4.47 & 3.10 \\ \hline \multirow{3}{*}{Knee angle during heel strike (\({}^{\circ}\))} & No risk & 14.38 & 10.70 \\ \cline{2-5}  & At risk & 13.90 & 8.10 \\ \cline{1-1} \cline{2-5}  & No risk & 24.52 & 8.40 \\ \cline{1-1} \cline{2-5}  & At risk & 22.85 & 10.90 \\ \hline \end{tabular}
\end{table} 
Table 2: Results of gait analysis according to fall risk. The resulting database consists of 1129 samples, discarding cases where acquisition errors were present. The information collected from each subject consists of age, gender, and the calculation of the eight gait indicators for both legs, as defined in Section 2.6.1. These are complemented by the Tinetti score, which is used as a reference for the desired output of the system. To classify the cases, an ANN is implemented using ReLU as the activation function for the hidden layers, softmax for the output layer, and categorical cross-entropy as the loss function. For training and validation, a 5-fold cross-validation method is used to divide the data between training and validation at 80% (904 samples) and 20% (225 samples), respectively. The performance of the resulting algorithm is evaluated in terms of accuracy, precision, recall, specificity, and F1-Score using the following equations:  
\[Accuracy=\frac{TP+TN}{TP+FP+TN+FN} \tag{12}\]  
\[Precision=\frac{TP}{TP+FP} \tag{13}\]  
\[Recall=\frac{TP}{TP+FN} \tag{14}\]  
\[Specificity=\frac{TN}{FP+TN} \tag{15}\]  
\[F1-Score=\frac{2(Precision)(Recall)}{Precision+Recall} \tag{16}\]  
where \(TP\) is the true positives that occur when the output corresponds to the correct class, \(FP\) is the false positives that occur when a case is mistakenly placed in another class, \(TN\) is the true negatives that are cases that are assigned to the class but do not belong, and \(FN\) is cases that belong to the class but their output does not correspond to the correct class. To define the structure of the algorithm, a trial-and-error process was used to determine the number of hidden layers and the perceptrons present in each, using ReLU as the activation function. Table 3 shows a synthesized representation of the proposed structures, along with their performance during validation. Figure 6: Division of the signals into 5 s windows, visually represented by the signal shown in blue and the divisions in red. The structure of test 4 is considered since it is the least complex structure and has a good performance.