## 3 Results
### Accuracy Assessment of Spatial Decomposition Results Using Twelve Regression Models
The statistics for the proportion of cell numbers in the twelve model outputs are shown in Figure 4.  
Among the decomposition results generated by the twelve regression models, the proportion of cells with a population density of less than 17,000 people/km\({}^{2}\) exceeded 90% (see Figure 4). In the decomposition results from the BSR model, the proportion of cells with a population density of less than 17,000 people/km\({}^{2}\) was the highest, about 96.76%. In contrast, in the decomposition results from the RF model, the proportion of cells with a population density of less than 17,000 people/km\({}^{2}\) was close to 91.6%, which was the lowest. The proportion of subdistricts with different relative errors in the twelve model results is shown in Figure 5. As can be seen in Figure 5, the proportions of subdistricts with different relative errors derived from the twelve models varied. Generally speaking, when the RE value of the model was in the range of \(-\)30% and 30%, it can be considered that the model prediction was sufficiently accurate. When the RE value of the model output was higher than 30%, it can be considered that the predicted population was overestimated. When the RE value of the model output was less than \(-\)30%, it can be considered that the predicted population was underestimated. The proportion of subdistricts with RE between \(-\)30% and 30% in the model output can be used to evaluate how many subdistricts present reasonable accuracy. The number of subdistricts with RE between \(-\)30% and 30% in the RF model output was the highest (there were 53 subdistricts within the range) while that of the BSR model was the lowest (only 25 subdistricts fell within the range). When the relative error value of the model output was higher than 30%, it can be considered that the predicted value was overestimated. In the decomposition results from the OLS model, 68 subdistricts demonstrated a relative error value higher than 30%, which accounted for 64.1% of the total number of subdistricts. In addition, there were 61 subdistricts with a relative error higher than 30% in the decomposition results from the Lasso model, which accounted for 57.5% of the total number of subdistricts. This result implied that the OLS model and the Lasso model both displayed a serious tendency to overestimate the population density. It is worth mentioning that in the spatial decomposition results from the OLS model, the number of subdistricts with an RE  
Figure 4: Grouping statistics for the proportion of cells with different population densities. greater than 30% accounted for more than 64%, which may be the main manifestation of the poor accuracy of the OLS model. In the decomposition results from the BSR model and the RANSAC model, the number of subdistricts with an RE higher than 30% were 28 and 29, respectively. Therefore, it can be considered that the BSR model and the RANSAC model were regression models with a lower tendency towards overestimation. The quantity of subdistricts with an RE of less than \(-30\%\) in the decomposition results from the OLS model was 7, which was the lowest of all the models. In contrast, the number of subdistricts with an RE of less than \(-30\%\) in the decomposition results from the BSR model was 53, which was the highest of all the models. These results may imply that the BSR model had a serious tendency towards underestimation. In summary, compared with that of the linear regression models, the accuracy of the non-linear regression models, RF, KNN, and SVR, was superior. Because the best performance was observed in the KNN model, the spatial decomposition results of the demographic data from the KNN algorithm are discussed in the following text. The gridded population map derived from the KNN model is shown in Figure 6 (overlayed by the boundary of subdistricts rendered with a light gray dotted line). Figure 5: Grouping statistics for the proportion of subdistricts with different relative errors. Figure 6: Gridded population map derived from the KNN model.