## 4 Discussion and Conclusions
### Discussion
#### 4.1.1 Principal Findings and Meaningful Implication  
1. The methodology framework proposed in this paper provides an effective and rapid approach to the fine spatial decomposition of demographic data. The auxiliary data from various sources can be combined for gridded population mapping via machine learning regression. It was demonstrated that location-based services (LBS) data, derived from mobile phones, Baidu map, Tencent LBS, Sina Weibo, and so on, offer the possibility of illustrating gridded population maps more accurately and finely in urban areas [11; 22; 64; 65; 66; 67; 68; 69; 70; 71]. In particular, the accuracy of gridded population maps can be improved significantly through the integration of remote sensing data and LBS data [72]. The geographical detector model can quickly and effectively identify the factors influencing population density distributions. Three non-linear machine learning regression algorithms, including the SVR model, the RF model and the KNN model, were employed in the spatial decomposition of demographic data, which was demonstrated to be useful for mining implicit non-linear relationships. The proposed approach can provide very useful information to support future research on the spatial decomposition of demographic data with growing multi-source geospatial data [22; 73].
2. The results of this study indicate that the OLS model is prone to overfitting in the spatial decomposition of demographic data. As we know, bias and variance are two key characteristics of estimators that must be considered in regression analysis; the former measures the accuracy of the model, while the latter measures the stability of the model. Clearly, ordinary least square linear regression is more affected by variance due to the excess of independent variables or collinearity. Both regularization and subsetting methods can effectively improve overfitting in the OLS model. Because all possible feature combinations are traversed, the features selected by the BSR model should, theoretically, offer an optimal combination. However, in this case, the improvement effect of the regularization methods on overfitting was better than in the BSR model, whether in the L1 regularization or the L2 regularization. These results again reflected the shortcomings of the BSR model. The reason why the BSR model is not the best in practical applications is still unclear; the unreasonable selection of independent variables, collinearity, and so on, are worth considering in this regard. In addition, another drawback of the BSR model is that it needs to fit 2P models, which is very computationally expensive (assuming the model includes p features). For this reason, we believe that for the spatial decomposition of demographic data, the regularization method is better than the subsetting method in improving overfitting.
3. The results of our case study demonstrate that for the spatial decomposition of demographic data, nonlinear regression models offer greater accuracy than linear regression models. The results may imply that the relationship between population density distribution and impact factors is complicated and non-linear. Since the nonlinear regression model can deal better with the collinearity of independent variables and other problems that easily lead to overfitting, we suggest that when conducting research on the spatial decomposition of demographic data, priority should be given to using nonlinear regression models to improve the accuracy of results. However, the results of regression models such as the KNN model, the SVR model and the RF model are non-parametric, and the interpretability of these models is very poor. Therefore, when the interpretability of the model needs to be taken into account, linear regression models based on the regularization method should be given priority.