## 2 Method
### Data Preprocessing
\begin{split}&\max\left[\sum\limits_{i=1}^{m}\alpha_{i}-\frac{1}{2} \sum\limits_{i,j=1}^{m}\alpha_{i}\alpha_{j}y_{i}y_{j}(x_{i}\cdot x_{j})\right] \\ & s.t.\sum\limits_{i=1}^{m}\alpha_{i}y_{i}=0,0\leq\alpha_{i}\leq C,i=1,2,...,m\end{split}  \tag{7}\]

Since the training samples are linearly inseparable, the original sample can be transformed into a high-dimensional space by introducing a kernel function method using nonlinear mapping. That is, the linear inseparable problem in the low-dimensional space is transformed into the linearly separable problem in the high-dimensional space. Common kernel functions are shown in Table 2:Choosing a suitable kernel function, the optimal classification function can be obtained:

\[f(X)=sign\left[\sum_{i=1}^{m}\alpha_{i}^{*}y_{i}K(x_{i},x)+b^{*}\right] \tag{8}\]

#### 2.4.2 Multi-Classification Method of SVM

The classic SVM only gives a two-class classification algorithm, so extending the support vector machine to a multi-class classification problem and obtaining significant results is still challenging. When using SVM to construct multi-class classifiers, two methods are usually applied. One is to extend to a multi-class classification support vector machine. This method uses a large number of variables and has high computational complexity, which is not applicable in reality. The other is to convert into a two-class classification problem using several two-class classification support vector machines to form a multi-class classifier. Due to the fast calculation speed, this method is widely used. This method has two typical algorithms called the \"one-against-all\" algorithm and the \"one-against-one\" algorithm. The \"one-against-all\" algorithm sequentially classifies the samples of a specific category into one category and other remaining samples into another category. In this way, the sample of \(N\) categories constructs \(N\) second-class classifiers. When classifying, the samples to be tested are classified into the category with the largest classification function value. Although this algorithm has the advantages of a small number of classifiers and a fast classification speed, due to the large difference in sample size between the two types, it is easy to cause the problem of dataset skew. At the same time, the \"one-against-one\" algorithm uses the training samples of any two categories to train a two-class classifier without repetition. For a multi-class classification problem with \(N\) categories of training samples, a total of \(N*(N-1)/2\) second-class classifiers is required. Although the number of classifiers in this algorithm is large, the training scale of a single second-class classifier of this algorithm is small, and the training data are balanced and easy to expand. In this paper, the \"one-against-one\" algorithm is applied to construct a multi-class classifier. ## 3 Results and Discussions

### Experimental Setting

#### 3.1.1 Data Source

The dataset used in this paper comes from the UCI database. The \"Simulated Falls and Daily Living Activities Data Set\" [31] included in the database in June 2018 was chosen for our experiment. The dataset was completed by 17 volunteers, including ten men and seven women. Each volunteer must complete 36 behaviors, including 20 falling behaviors and 16 daily behaviors, each repeated five times. In this way, there are 3060 sampled data for each part. The original signal is a total of 21-dimensional signals such as three-dimensional acceleration, three-dimensional angular velocity, three-dimensional velocity, three-dimensional geomagnetism, pressure, and more output from the sensor. The sensor's sampling frequency is 25 Hz, and the average sampling time for each action is 15 s. It has been shown that breasts can achieve better recognition accuracy [32]. In this paper, we select all samples of breasts in this dataset as raw data. Figure 3 shows the change of the sensor value during front-knees and back-lying actions. It can be observed that