## 5 Data Processing and Results
### Projection of Future Coordination Degree
#### 5.7.2 Gradient Boosting Regression  
Figure 31 shows the results of the training and testing performance using \(R^{2}\) using our dataset \(O\). As can be seen, the training performance is superb, with all but one region has nearly perfect \(R^{2}\). However, the generalizability is extremely poor, with the testing \(R^{2}\) being negative for all regions. Obviously, the gradient boosting regression is not suitable for making projections.  
The patterns of performance on training and testing remain similar for the coordination degrees using the reference dataset \(R\) as shown in Figure 32. While the training performance is noticeably improved over the linear regression with polynomial features, the testing performance is actually worse, with no region having positive \(R^{2}\).  
For completeness, we show the actual coordination degree and the predicted value for the same two regions, Beijing and Sichuan, using our dataset 0, in Figure 33. The insets  
Figure 31: GBR training \(R^{2}\) and testing \(R^{2}\) for the coordination degrees using our dataset \(O\).  
Figure 32: GBR training \(R^{2}\) and testing \(R^{2}\) for the coordination degrees using the reference dataset \(R\).  
are zoomed-in for the five-year projection. As can be seen, GBR has excellent regression performance for the training set but performs poorly for projection using the testing set.  
Figure 34 shows the actual coordination degree and the GBR-predicted value for two regions, Hainan and Sichuan, using the reference dataset \(R\). As can be seen, again, the regression errors are much larger than those using our dataset \(\mathcal{O}\).  
Similar to LRPF, besides \(R^{2}\), the regression and projection performance can also be evaluated in terms of mean absolute error (MAE) and root mean squared error (RMSE). For completeness, we show the performance evaluation in terms of MAE and RMSE, for both our dataset \(\mathcal{O}\) and the reference dataset \(R\) in Figures 35-38.  
Using MAE as the performance evaluation metric, we can see from Figures 35 and 36 that the training error is several folds bigger for the reference dataset \(\mathcal{R}\) than for our dataset \(\mathcal{O}\). However, the testing errors for the two datasets are on the same scale.  
Using RMSE as the performance evaluation metric, we can see from Figures 37 and 38, the patterns are roughly similar to those for MAE. The testing error for the reference dataset \(\mathcal{R}\) is slightly larger than that for our dataset \(\mathcal{O}\).  
Again, we can see that \(R^{2}\) is a more distinctive metric on the quality of regression and projection because the contrast between training and testing, as well as the contrast between the performance of the two datasets are much more prominent.  
Figure 34: The actual data and the GBR-predicted values using the reference dataset \(\mathcal{R}\) for Hainan and Sichuan.  
Figure 33: The actual data and the GBR-predicted values using our dataset \(\mathcal{O}\) for Beijing and Sichuan.  
Figure 37: GBR training RMSE and testing RMSE for the coordination degrees using our dataset \(O\).  
Figure 35: GBR training MAE and testing MAE for the coordination degrees using our dataset \(O\).  
Figure 36: GBR training MAE and testing MAE for the coordination degrees using the reference dataset \(R\).