# Data Transmission in Wireless Sensor Networks Based on Ant Colony Optimization Technique
## 2 Materials and Methods
### Increase the Coverage of WSNs  
We use a newly added optimized clustering method to determine WSN clustering. In wireless sensor network clustering, the number of clusters and initialization centers are uncertain and need to be improved. Figure 8: Multiple WSN optimization paths. Figure 7: An optimization path. It is important to note the adjustment of parameters:  
When T1 is too large, it can cause many points to belong to multiple canopies, which may result in closer distances between the center points of each cluster and less obvious differences between clusters. When T2 is too large, increasing the number of strongly labeled data points will reduce the number of clusters; if T2 is too small, it will increase the number of clusters and also increase the calculation time. Optimizing clustering methods to determine WSN clustering  
Optimize the selection of initial cluster centers  
As shown in Figure 10, if cluster centers are too dense, most data points will form a cluster. Clustering centers that are too scattered can lead to sparse data points and unreasonable classification. Choosing the optimal cluster center is crucial. An excellent cluster center needs to meet the high density of nodes around the cluster center and the long distance between each cluster center. Data point collection is as follows: \(X=\left\{X_{1},X_{2},\cdots,X_{n}\right\}\). Calculate the average distance between all data points as follows:  
\[AveDis=\frac{2}{n(n-1)}\sum_{i=1}^{n}\sum_{j=i+1}^{n}d\left(X_{i},X_{j}\right) \tag{4}\]  
In the formula, represents the distance between two points. \(d\left(X_{i},X_{j}\right)\) represents the distance from node \(X_{i}\) to node \(X_{j}\), \(n\) represents the maximum number of wireless sensor nodes, and \(AveDis\) represents the average distance between all nodes. When the number of cluster centers and the total cluster area are determined, the ideal radius for obtaining clusters is as follows:  
\[\text{R}=\frac{S}{n} \tag{5}\]  
Data point density  
Figure 10: Clustering of the canopy algorithm. Calculate the standard deviation of the distance between each data point and other data points as the density of that data point. The density of the data point is \(density_{i}\), calculated as follows:  
\[density_{i}=\frac{\sqrt{\sum_{j=1}^{n}\left(d\left(X_{i},Y_{i}\right)\ -AveDis \right)^{2}}}{\sqrt{n-1}} \tag{6}\]  
The basic idea for selecting the initial clustering center for data point density is to use the data point with the highest density as the first initial clustering center \(C_{1}\). Then, calculate the distance from the remaining data points to \(C_{1}\) (Euclidean distance); if the distance is less than the average distance \(AveDis\) between each data point, then move it into the class of \(C_{1}\). Then, select the data point with the highest density from the data points outside the cluster radius of the first initial cluster center \(C_{1}\) as the second initial cluster center \(C_{2}\), and continue the cycle until k initial cluster centers are selected. The specific steps for selecting the initial cluster center are as follows:  
Initialize the parameter \(k\), cluster radius \(r\), and data point set \(X\);  
Calculate the average distance between all non-cluster-center data points in \(X\) according to Formulas (1) and (3) \(AveDis\) and the data point density \(density\) in \(X\);  
Select the data point with the highest density among all data points as the first cluster center \(C_{1}\). Select the data point with the highest density of data points outside the initial cluster center I and cluster radius J as the second cluster center \(C_{2}\);  
Continuously perform steps 2, 3, and 4 until \(k\) initial cluster centers are selected. Improve the K-means algorithm process  
Combine the canopy algorithm with the K-means algorithm to improve the K-means algorithm process.