## 2 Method
### Data Preprocessing
 \tag{10}\]2.1 Result 1: Comparison between before and after Feature Extraction of WPT Using Different Classifiers

In order to verify the effectiveness of the proposed wavelet packet decomposition method in feature extraction and the recognition and classification of SVM, comparison between the sample set formed by the time-domain feature vector combined with the feature vector obtained by wavelet packet decomposition with the sample set that only uses the time-domain feature vector were conducted. At the same time, the SVM based on linear kernel function (Linear_SVM), SVM based on radial basis function (Rbf_SVM), Xgboost, LogisticRegression and KNN are used for the recognition and classification of fall posture. The classification of the selected 16 ADLs and 12 fall behaviors are shown in Table 3. In order to better evaluate the prediction performance of the model, the experimental results all adopted a five-fold cross-validation method, and finally, the fall posture recognition results of different classifiers are shown in Table 4. We observed that, regardless of whether we used the time-domain feature or the wavelet packet transform feature combined with the time-domain feature, the accuracy, recall, f1 score, and precision of the SVM with the linear kernel function reached the highest. In addition, we can see that for each classifier, after adding the features obtained by the wavelet packet transform, the accuracy, recall, f1 score, and precision were greatly improved. In order to test the significance of the differences as mentioned above, this paper used the multi-factor analysis of variance to test the significance of the differences in the experimental results using wavelet packet transform and different classifiers, for which the significance level \(\alpha\) is set to 0.05; if the p-value was less than the \(\alpha\), it means that there is a statistically significant difference in the above results. The experimental results are shown in Table 5. The results indicate that SVM has significant advantages in solving the problem of small samples and high-dimensional features, and it also confirms the effectiveness of the wavelet packet transform in feature extraction. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number** & **Behavior Description** & **Type** \\ \hline
801 & walking forward & \\
802 & walking backward & \\
803 & jogging,running & \\
804 & squatting, then standing up & \\
805 & bending about 90 degrees & \\
806 & bending to pick up an object on the floor & \\
807 & walking with a limp & \\
808 & stumbling with recovery & \\
809 & bending while walking and then continuing walking & \\
810 & coughing or sneezing & \\
811 & to sitting with a certain acceleration onto a chair (hard surface) & \\
812 & to sitting with a certain acceleration onto a sofa (soft surface) & \\
813 & to sitting in the air exploiting the muscles of legs & \\
814 & to sitting with a certain acceleration onto a bed (soft surface) & \\
815 & from vertical lying on the bed & \\
816 & from lying to sitting & \\ \hline
901 & from vertical falling forward to the floor & \\
902 & from vertical falling forward to the floor with arm protection & \\
907 & from vertical falling down on the floor, ending in right lateral position & front-lying \\
908 & from vertical falling down on the floor, ending in left lateral position & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Classification of the selected 16 ADLs and 12 fall behaviors. #### 3.2.2 Result 2: Comparison before and after Feature Selection

Combining the extracted time-domain features and wavelet packet features as a new sample set can further improve the classifier's recognition accuracy. However, the feature dimension is too high. Only certain features can help the classifier perform classification and recognition. The remaining features will affect the recognition accuracy and cause a tremendous waste of computing resources and time.