# Fall Detection Approaches for Monitoring Elderly HealthCare Using Kinect Technology: A Survey
## 5 The Performance Measurement Terms  
The performance of a fall detection approach is measured using standard terms. In particular, these terms verify how often the judgments of the system are correct given the actual situation of events. The fall detection problem can be considered as a binary detection/classification problem. The confusion matrix and its derivations are the most frequently used measurement tools to assess the quality of a fall detector [113; 114]. In this section, we explain the terms of performance used in the reviewed papers, providing the general definition of each measurement and its application in fall detection algorithms. Before going into details, we note that these terms are used to set thresholds as well as in machine learning and deep learning approaches. We use the prediction and observation or class terms for all types of algorithms. To measure the total performance, it is necessary to have the four components of the confusion matrix: true positive (TP), true negative (TN), false positive (FP), and false negative (FN). A TP is a result where the algorithm correctly predicts the positive observation. Similarly, a TN is a result where the algorithm correctly predicts the negative observation. Likewise, FPs and FNs are outcomes where the model incorrectly predicts the positive and negative classes. Because true and false observations are known in almost all fall detection papers for the real-life situation of falls and ADLs, respectively, the TPs and FPs respectively count the number of falls and ADLs detected as falls. The same counting principle applies to TNs and FNs. Table 4 explains the distribution of terms for each situation. The table's columns correspond to the actual situation of actions, and every row is linked to the result of the algorithm. The confusion matrix exposes how the approach is confused when it judges scenarios detected by intelligent devices. It provides an explanation of the types of errors made by the system. Several evaluation measures based on the confusion matrix elements are defined. These are used to quantify the performance from different perspectives [115]. The total number of observations successfully detected is known as accuracy. It proves the success rate of fall detection approaches. However, it only reflects the reality of the system when working on symmetric datasets, where there is npo disproportion between the number of real situations (i.e., falls and ADLs). \[\text{Ac}=\frac{\text{TP}+\text{TN}}{\text{TP}+\text{TN}+\text{FP}+\text{FN}} \tag{1}\]  
The error rate (misclassification rate) represents the ratio of incorrectly detected observations to the total amount of data, or simply one minus the accuracy. It demonstrates how often the fall detection algorithm is wrong. \[\text{ERR}=\frac{\text{FP}+\text{FN}}{\text{TP}+\text{TN}+\text{FP}+\text{ FN}} \tag{2}\]  
Precision is the ratio of correctly positive predictions to the number of predicted positive observations. It determines the percentage of actions identified as falls that have \begin{table}
\begin{tabular}{c c c c} \hline \hline  & & **Real Situation** \\ \hline  & & **Fall** & **No-Fall/ADLs** \\ \hline
**predicted** & **Fall** & TP & FP \\
**situation** & & & \\ \hline  & **No-fall/ADLs** & FN & TN \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Confusion matrix. been detected correctly. This performance expression allows for judging the stability of a fall detection algorithm. \[\text{Pr}=\frac{\text{TP}}{\text{TP}+\text{FP}} \tag{3}\]  
The sensitivity (recall, recognition rate, or true positive rate) can be defined as the proportion of actual positive results that have been correctly detected. In other words, this metric measures how useful the algorithm is in identifying the falls movement. \[\text{Se}=\frac{\text{TP}}{\text{TP}+\text{FN}} \tag{4}\]  
Specificity (selectivity or true negative rate) is the proportion of actual negatives outcomes that have been correctly identified. It shows the ability of algorithms to recognize ADLs and avoid false alarms correctly.