## 4 Performance Investigation
It also has 40% higher performance than the optimized k-means algorithm based on LEACH. The reason for the performance difference is that the LEACH algorithm randomly chooses cluster-heads without regarding the located site and remaining energy of cluster-heads in the network. The proposed LEACH-K algorithm designates the node nearest to the cluster centroid as the cluster-head. However, in most implementations, the remaining energy of the node and its distance to its sink node are not considered. It can be concluded that the proposed LE-KCR algorithm is more durable than the other two algorithms before the network is disconnected. Figure 5: The number of dead nodes vs. different transmission rounds. Figure 7 presents the change in node remaining energy variance when the LEACH, the LEACK K-Means, and the proposed LE-KCR algorithms are employed. As depicted in Figure 7, the proposed LE-KCR algorithm has a better performance of energy balance than both the LEACH and the LEACK K-Means algorithms with different transmission rounds. With the increase in the number of simulation rounds, the variance of remaining energy shows an upward trend. For instance, when the number of transmissions is as low as 27, more than half of the nodes die in network when running the LEACH, which will automatically be disconnected. The variance of LEACH before disconnection and LEACH-K after 70 rounds is about 2200. However, the LE-KCR variance after 100 rounds of operation is about 700, only 1/3 of LEACK-K. This proves that the proposed LE-KCR strategy is also significantly better than the other two algorithms in energy balance. Figure 8 presents the change in the death rate of nodes when the different network sizes are employed. As revealed in Figure 8, the change in network size has little impact on node mortality. We set the number of different nodes and calculate the node mortality after 300, 500, and 800 rounds of simulation. We can see that with the increase in simulation  
Figure 6: Remaining energy vs. different transmission rounds. Figure 7: The variance of remaining energy vs. different transmission rounds. rounds, the node mortality of the network with the same number of nodes will increase significantly. However, with the increase in network scale, after 300, 500, and 800 rounds of network simulation, the node mortality fluctuates up and down at 0.11, 0.25, and 0.4, respectively. Due to the randomness of the nodes' located site, the network is different in the simulation. Therefore, the statistical mortality rate will fluctuate to a certain extent, but within a reasonable range. This proves that the performance of the proposed LE-KCR will not be greatly affected by the change in network scale. Noticeably, this paper assumes that the position of sensor nodes does not change. However, in the actual deployment, due to the influence of water flow, it will lead to the swing of nodes and the change in node position. Therefore, it is necessary to combine the underwater node positioning algorithm to update the latest coordinates of the node in reality. Meanwhile, the water flow will also bring coordinate errors to the position estimation of anchor nodes. We plan to further this research as mentioned above in future work.