## 2 Method
### Data Preprocessing
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Kernel Function** & **Kernel Function Expression** & **Parameter** \\ \hline Linear kernel & \(K(X_{i}\cdot X)=(X_{i}\cdot X)\) & - \\ Polynomial kernel function & \(K(X_{i}\cdot X)=[s(X_{i}\cdot X)+c]^{d}\) & \(s,c,d\) \\ Radial basis function & \(K(X_{i}\cdot X)=\exp\left(-g\|X-X_{i}\|^{2}\right)\) & \(g\) \\ Sigmoid kernel function & \(K(X_{i}\cdot X)=\tanh[s(X_{i}\cdot X)+c]\) & \(s,c\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Common kernel functions in SVM. different sensors produce different signals. Thus, different fall postures can be identified by extracting the change characteristics of different sensors' signal values. Figure 3: Examples of sensor signals for a front-knees action and a back-lying action: (**a**) front-knees, acceleration; (**b**) back-lying, acceleration; (**c**) front-knees, gyroscope; (**d**) back-lying, gyroscope; (**e**) front-knees, magnet; (**f**) back-lying, magnet; (**g**) front-knees, Euler angle; and (**h**) back-lying, Euler angle. #### 3.1.2 Data Division

There are 20 fall behaviors in the original data, of which we selected 12 behaviors. In the unused fall data, the four actions numbered 905, 906, 914, and 916 are those the tester would quickly or slowly recover after a fall, which shows that this type of fall does not cause the user to lose control of their body, so it is beyond the scope of our research. The remaining four behaviors numbered 917, 918, 919, and 920 did not indicate the fall's direction and posture, so these four datasets were discarded. In addition, this paper's focus is to recognize the posture when falling, and the 16 daily behaviors were classified into one category, and no further subdivision was required. Finally, the selected 12 fall behaviors and 16 daily behaviors were classified into seven different behaviors, which were ADLs, front-lying, front-knees, back-lying, back-sitting, fall to the left, fall to the right. #### 3.1.3 Experimental Platform

The research on the falling posture recognition and classification algorithm based on machine learning was completed on the Windows10 operating system; we used the PyCharm 2019.2.2 (Community Edition) as software, and the CPU type was Intel Core i5-4200H @2.80 GHz. ### Experimental Results

Based on the \"Simulated Falls and Daily Living Activities Data Set\", this paper extracted 12 fall actions and 16 ADLs such as standing, walking, squatting, and a total of 3060 samples to test the proposed fall posture recognition method. It was pointed out that [33] there is no common standard for evaluating the effect of fall posture recognition at this stage, and it is challenging to perform effect testing based on general procedures. In this paper, accuracy, recall, f1 score and precision were used to evaluate the testing effect. There are four basic symbols: true positive (_TP_): successfully predict positive samples as positive, true negative (_TN_): successfully predict negative samples as negative; false positive (_FP_): wrongly predict negative samples as positive; false negative (_FN_): wrongly predict positive samples as negative. For multi-classification problems, the macro method can be used. The accuracy, precision, recall, and f1 score can be expressed as

\[Accuracy=\frac{TP+TN}{TP+TN+FP+FN} \tag{9}\]

\[ \begin{split} Precision=\frac{TP}{TP+FP}\\ macro-Precision=\frac{1}{n}\sum_{i=1}^{n}Precision_{i}\\ \\ Recall=\frac{TP}{TP+FN}\\ macro-Recall=\frac{1}{n}\sum_{i=1}^{n}Recall_{i}\\ \\ F_{1 score}=\frac{2*Precision*Recall}{Precision+Recall}\\ macro-F_{1 score}=\frac{1}{n}\sum_{i=1}^{n}F_{i}\\ \end{split}