# Entity Embeddings in Remote Sensing: Application to Deformation Monitoring for Infrastructure
## 4 Results and Discussion
### Comparison of EE-DL, GPR, and RF  
The results of the EE-DL and GPR approaches were compared to the baseline model, RF. The global error between the measured and predicted deformation at test time is plotted in Figure 10. As expected, the simplest approach, RF, performed the poorest. It has a consistently high RMSE for all test dates compared to the other models in Figure 10a. The best-performing model was GPR, which had the lowest RMSE for all the time steps. The EE-DL performance was intermediate between RF and GPR for all dates. The RMSEs were approximately up to \(\pm\)4 mm and were similar to the absolute error related to the background prediction noise level in Figure 6. A value of \(\pm\)4 mm is consistent with the background noise level of InSAR measurements reported in previous studies, e.g., [52; 53]. Therefore, an error envelope of 8 mm was adopted as a threshold for separating normal from anomalous deformation behaviour. Similar to the RMSE results, the Maximum Error (MAXE) was also highest for RF. In Figure 10b, RF consistently has the highest MAXE for all dates. Interestingly, the shape of the MAXE was consistent for the last three dates for all the models, which gave the highest MAXE for 2018-02-13 and the lowest immediately preceding the failure in 2018-02-25. A spatial visualisation of the anomalous clusters captured by the various models is given in Figure 11a-c. These maps show that all models successfully captured anomalous clusters in the failure area of the northern TSF. It is clear that the anomalous clusters in Figure 11 for (a) EE-DL and (b) GPR are much more focused around the slump area compared to (c) RF. Figure 11c, RF, contains many anomalous clusters outside the immediate slump area, spreading to all parts of the northern TSF. This large spread of anomalous  
Figure 10: Global error metrics for the various models. (**a**) RMSE and (**b**) Maximum Error (MAXE). clusters does not assist in narrowing down the area of potential problems. The RF model also detected a small number of anomalous clusters in the stable, south TSF. The anomalous cluster 1 in Figure 11c was only detected by RF and not the other two approaches, potentially limiting its reliability, whereas cluster 2 was detected by all models, giving more confidence to its anomalous nature. Figure 11: Spatial distribution of anomalous clusters detected on the last four test dates for (**a**) EE-DL, (**b**) Gaussian Process Regression mean, and (**c**) Random Forest baseline model. The failure area of the northern TSF is outlined. Slumping occurred in two stages; the black outline precedes white. Basemap image copyright © 1995–2020 Esri. All the algorithms detected some false positives. Thus, it is important to note that not all the instances flagged as false positives in Figures 11 and 12 are necessarily incorrect in identifying anomalous behaviour. Even though these measurements were outside the slump area, they may still exhibit true anomalous behaviour that is unrelated to failure, for instance anomalous behaviour stemming from other construction processes. Interpreting the location and temporal occurrence of anomalies outside the slump area is beyond the scope of this study. Further clarification may be gained from combining InSAR with other data sources. The definition of true and false positives was intentionally simplified to enable a clear and concise comparison of the wide spectrum of algorithms employed in this study. Moreover, the number of true and false anomalies detected by the various models was counted and is summarised in Figure 12. It shows that EE-DL detected the most true anomalous clusters, with a total of 69 compared to 59 by RF and 26 by GPR. It is also clear in Figure 12 that the RF model consistently detected the most false positives, a total of 177 compared to 59 for EE-DL and 30 for GPR. Moreover, the RF model had a higher number of false positives than true positives for all dates, potentially limiting its ability to locate the failure area.