# Animal Movement Prediction Based on Predictive Recurrent Neural Network
## 4 Experiments
### Movement Prediction
As mentioned above, we consider ten different cases in the experiment by grouping unit, input days, and output days and calculated the average for each metric. Table 7 shows the results, in which our prediction model showed the best performance from case 1. To evaluate the performance of our model, we compare it with vector auto regressive model (VAR), which is known to be useful for time-series prediction. In the comparison, we calculate the movement centroids using the Gaussian mixture fitting and use them as input values of the VAR. To construct VAR, we used the R package 'VARS' and utilized the 'VARselect' function to find out the most appropriate setting for VAR fitting. The comparison results are as follows. From these Tables 8-10, we can see that our model outperforms VAR in most cases. In particular, our model, when trained using movement patterns of short observation period, showed better performance. In summary, our model can cover long range and short range predictions and hence can be used to predict not only seasonal movements such as strong migration but also typical movements such as foraging and roaming. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Evaluation Metrics**} \\ \cline{2-6}  & **Avg.** & **Avg.** & **Avg.** & **Avg. Centroid** & **Avg. Centroid** \\  & **MSE** & **RMSE** & **SSIM** & **Distance (in pixels)** & **Distance (in km)** \\ \hline Case 1 & 44.236 & 6.651 & 0.970 & 4.583 & 110.179 \\ Case 2 & 44.571 & 6.676 & 0.965 & 5.299 & 127.413 \\ Case 3 & 51.090 & 7.148 & 0.963 & 5.586 & 134.299 \\ Case 4 & 58.142 & 7.625 & 0.958 & 7.028 & 168.983 \\ Case 5 & 72.445 & 8.511 & 0.937 & 8.492 & 204.182 \\ Case 6 & 43.445 & 6.591 & 0.968 & 4.698 & 112.944 \\ Case 7 & 43.182 & 6.571 & 0.962 & 5.037 & 121.099 \\ Case 8 & 53.219 & 7.295 & 0.953 & 5.487 & 131.933 \\ Case 9 & 62.847 & 7.928 & 0.943 & 7.602 & 182.779 \\ Case 10 & 142.449 & 11.935 & 0.932 & 10.265 & 246.795 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: MSE, RMSE, SSIM, and centroid distance measure results. Figure 9 shows an example of movement prediction. In the figure, for an input sequence in (a), (b) and (c) show the ground truth sequence and predicted sequence, respectively. The input and ground truth sequences represent the short-distance migration movement of long-billed curlews from 10 May 2018 to 23 May 2018. The short-distance migration occurs between pre-breeding season and breeding season. This figure demonstrates that our model predicts the density location of animal movements after one-day (T = 1) with an error range of approximately 23 km. That is, based on the density images of the last seven days, our prediction model generated the density images of next seven days. To analyze the prediction accuracy in more detail, we conducted daily comparison of RMSE, SSIM, and centroid distance results are shown in Table 11. In the table, we can see that overall prediction results are quite reasonable and that prediction for the first day is the best. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Metric**} & \multicolumn{6}{c}{**Prediction day**} \\ \cline{2-7}  & **8** & **9** & **10** & **11** & **12** & **13** & **14** \\ \hline RMSE & **6.913** & 7.816 & 7.491 & 6.622 & 7.337 & 7.719 & 6.532 \\ SSIM & **0.966** & 0.963 & 0.959 & 0.961 & 0.960 & 0.965 & 0.939 \\ Cent-Dist in pixels & **0.970** & 3.240 & 2.509 & 1.360 & 2.126 & 1.761 & 2.809 \\ Cent-Dist in km & **23.331** & 77.901 & 60.333 & 32.700 & 51.121 & 42.334 & 67.526 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Daily comparison of RMSE, SSIM, and centroid distance of case 1. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{4}{c}{**Evaluation Metrics**} \\ \cline{2-4}  & **RMSE** & **Avg. Centroid Distance (in pixels)** & **Avg. Centroid Distance (in km)** \\ \hline Case 1 & **6.872** & **4.583** & **110.179** \\ Case 6 & 6.914 & 4.698 & 112.944 \\ VAR & 10.573 & 12.840 & 308.695 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison results of Case 1, Case 6 and VAR.