# Improved Particle Swarm Optimization for Sea Surface Temperature Prediction
## 4 Results and Discussion
### Analysis of Experimental Results
In this paper, a local search strategy is used to enhance the local search capability of the PSO, so that the improved PSO has independent global and local search capabilities. Therefore, the obtained solution set has better convergence and more uniform distribution. **Experiment 3: Comparison of DSL performance with other SSTP methods. **_DSL is a combination of DTW + SVM (DS) and LSPSO. Define the space composed of the PL and the IS as the search space of the particle, and the prediction accuracy and efficiency set as the optimization objectives, LSPSO can compute the appropriate PL and IS that are set to the parameter of DS to predict SST. Here, we compare the performance of DSL with DTW, SVM, DS, LSTM in SSTP. In the situation of predicting 5-day SST with a given t-day of SST data, the DTW method is to find the most similar series of SST from historical data and take its following 5 days as the prediction. The SVM and LSTM both are trained by fitting nonlinear changes in SST. DS is to train a SVM by top-k similar series selected according to DTW._  
The comparison results are shown in Table 4. The average value of RMSE obtained by DS in predicting SST is 0.4468, which is lower than the average RMSE of the DTW. This indicates that the combination of DTW and SVM can effectively utilize the information after DTW mining. Secondly, the prediction results of the DS algorithm are better than those of SVM. This is because the SST sequence contains a lot of redundant information, which will interfere with the model during prediction, making the SVM prediction accuracy low. LSTM gains the average RMSE of 0.5211, which is worse than DTW, DS and DSL. Although LSTM is developed for dealing with long and short-term prediction problem, it does not work well in predicting SST. This is probably due to the non-stationarity of SST. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Station** & **DTW** & **SVM** & **DS** & **LSTM** & **DSL** \\ \hline
1 & 0.4866 & 0.7403 & 0.4640 & 0.5093 & 0.3255 \\
2 & 0.5136 & 0.7117 & 0.4979 & 0.5075 & 0.4056 \\
3 & 0.4606 & 0.7338 & 0.4387 & 0.4839 & 0.3334 \\
4 & 0.4637 & 0.8383 & 0.4569 & 0.5458 & 0.3454 \\
5 & 0.4544 & 0.6208 & 0.4259 & 0.4534 & 0.3862 \\
6 & 0.4630 & 0.8694 & 0.4414 & 0.5710 & 0.4300 \\
7 & 0.5204 & 0.8532 & 0.5121 & 0.5781 & 0.4816 \\
8 & 0.4429 & 0.7840 & 0.3936 & 0.5154 & 0.2924 \\
9 & 0.4161 & 0.7660 & 0.3911 & 0.5259 & 0.3534 \\ Avg & 0.4690 & 0.7686 & 0.4468 & 0.5211 & 0.3726 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: RMSE obtained when predicting SST by DTW, SVM, DS, LSTM and DSL. DSL obtains the optimal parameters of PL and IS by LSPSO, and uses them in DS to predict SST. Comparing the RMSE values between DS and DSL, it can be found that the performance of DSL prediction of SST is better than DS, indicating that the parameters of DS can be effectively optimized by LSPSO, which was responsible for a 16.7% improvement in prediction accuracy, in terms of reducing the RMSE. In summary, the overall effect of DSL prediction of SST is optimal, indicating that the method can effectively predict SST and verify the effectiveness of the proposed method. We demonstrated the predicted results by different SSTP methods. Figure 6 shows a sample, randomly selected from the results. The black line represents the true values; the blue line represents the predicted results by using DTW; the red and yellow lines correspond to SVM and LSTM, respectively; the predicted results by using DSL are shown in green. It is clear that the results predicted by our method (green) are the closest ones to ground truth (black), including also the trend changes. On the other hand, the change trend of the other methods fluctuates significantly. Finally, Figure 7 shows the operating efficiency of DS at predicting SST, before and after LSPSO optimization. RT represents the running time in seconds. The first nine columns provide RT for nine different SST sequences, with the average values given in the last column.