## 2 Method
### Second Step Selection  
Assume that \(X^{\prime}=(X_{1},X_{2},\ldots X_{v})\) is the feature vector retained in the first step; this is usually \(v\leq n\), because the original number of features is \(n\). Assume that \(\mathbf{X}_{i}\) is a feature vector in \(\mathbf{X}^{\prime}\) and the corresponding matrix of real features and labels \(G\) is expressed as follows:  
\[G=\left[ \begin{array}{cccc}(a_{1}^{(1)}|_{nor},Y_{1,1})&(a_{2}^{(1)}|_{nor}, Y_{1,2})&\ldots&(a_{m}^{(1)}|_{nor},Y_{1,m})\\ (a_{1}^{(2)}|_{nor},Y_{2,1})&(a_{2}^{(2)}|_{nor},Y_{2,2})&\ldots&(a_{m}^{(2)}|_ {nor},Y_{2,m})\\ \ldots&\ldots&\ldots&\ldots\\ (a_{1}^{(k)}|_{nor},Y_{k,1})&(a_{2}^{(k)}|_{nor},Y_{k,2})&\ldots&(a_{m}^{(k)}| _{nor},Y_{k,m})\end{array} \right] \tag{5}\]  
The clustering method is used to obtain cluster labels, and K-means, linkage, and gmdistribution are considered as alternatives, because the applicability of different data is different for clusteringalgorithms [27; 28]. K-means determines the optimal class by iteratively calculating the distance between the sample and the centroid. Linkage calculates the similarity of different data, and sorts them to obtain a category. Gmdistribution converges to a local optimum with iterative computation. The silhouette value criterion is taken to obtain the best clustering algorithm and algorithms switched for different types of data. 1. Silhouette value criterion The silhouette value describes the state of cohesion and the degree of separation, which is an important parameter for evaluating the effect of clustering [29; 30]. The range of silhouette values is between \(-1\) and \(1\); the larger the value, the better the clustering result. The concrete implementation steps are as follows: 1. Assume that \(x_{i}\) is one of the elements, calculating the distance between \(x_{i}\) and all of the other elements within its own cluster. Take the mean of the distance and denote it as \(a_{i}\), which is used to quantify the cohesion. 2. Randomly take another cluster \(b_{j}\), and calculate the average distance between \(a_{i}\) and all of the elements in the cluster \(b_{j}\). 3. Traverse all of the clusters and find the minimum average distance and denote it as \(b_{j}^{\prime}\), which is used to quantify the separation. 4. The silhouette value of \(x_{i}\) is \(s_{i}=(bt_{j}-a_{i})/max(a_{i},bt_{j})\). 5. Calculate the silhouette value of each element, and obtain the mean as the overall silhouette value of the current clustering. 2. The algorithm switching rule is as follows: 1. Select two features randomly in the feature vector as samples to carry an algorithm comparison; assume that the selected features are \(X_{u}\) and \(X_{w}\). 2. The optimal number of clusters needs to be determined firstly in order to compare the fitness of the three clustering algorithms. Since the numbers of the signal labels are \(m\), cluster and calculate the silhouette value using those three algorithms respectively. Then, average them when the number of clusters is \(2,3\ldots m\). Assume that the result is \(B_{u2},B_{u3}\ldots B_{nm}\) for \(X_{u}\), and the result is \(B_{u2},B_{u3}\ldots B_{nm}\) for \(X_{w}\). 3. Define \(B_{u}=max\{B_{u2},B_{u3}\ldots B_{nm}\}\) and \(B_{w}=max\{B_{w2},B_{u3}\ldots B_{nm}\}\). Let \(K_{u}\) equal the number of clusters corresponding to \(B_{u}\), and let \(K_{w}\) equal the number of clusters corresponding to \(B_{w}\); thus, \(K_{u}\) and \(K_{w}\) are the optimal number of clusters for each feature. 4. The selection of the optimal clustering algorithm can be started after determination of the optimum number of clusters. Take \(K_{u}\) as the number of clusters, carry out cluster analysis out on the feature \(X_{u}\), and assume the silhouette value is \(M_{u1}\), \(M_{u2}\), and \(M_{u3}\) when the clustering algorithm is K-means, linkage, and gmdistribution, respectively.