## 2 Materials and Methods
### Machine Learning Test Method  
Subsequently, the population densities of each cell unit were predicted using the best estimator. Next, the predicted population of each cell was obtained by multiplying the population density and the cell's area. Finally, the predicted population of each subdistrict was obtained by merging the cell's population with the scope of the subdistrict. \begin{table}
\begin{tabular}{c c} \hline \hline
**Type** & **Factors** \\ \hline \multirow{8}{*}{Natural factors} & (I) POI density: X1 (Government agencies), X2 (Public service facilities), X3 (Commercial residential facilities), X4 (Medical service facilities), X5 (Financial facilities), X6 (Transportation facilities), X7 (Educational, scientific, and cultural facilities), X8 (Sports and leisure facilities), X9 (Living service facilities), X10 (Catering facilities), X11 (Companies), X12 (Accommodation service facilities), X13 (Shopping facilities) (2) Night light intensity: X14 (Night light intensity index) (3) Building area: X17 (Building area index) (4) Road intensity: X20 (Road density index) \\ \hline \multirow{4}{*}{Socio-economic factors} & (5) Land use: X15 (Index of urban land use), X18 (Index of arable land), X19 (Index of wood land), X21 (Index of rural land), X22 (Index of other construction land), X23 (Index of waters), X24 (Index of grass land) (6) Altitude: X16 (Elevation index) \\ \cline{1-1} \cline{2-3}  & (5) Land use: X15 (Index of urban land use), X18 (Index of arable land), X19 (Index of wood land), X21 (Index of rural land), X22 (Index of other construction land), X23 (Index of waters), X24 (Index of grass land) \\ \cline{1-1} \cline{2-3}  & (6) Altitude: X16 (Elevation index) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Initial influence factors. The accuracy of the prediction results was evaluated using five commonly-used metrics, including mean absolute biased error (MABE), mean absolute percentage error (MAPE), root mean square error (RMSE), relative error (RE), and coefficient of determination (R2), taking the demographic data as the basis for evaluation. All the algorithms used in this paper were implemented in the scikit-learn 0.24.0 software, except for the BSR method. A brief introduction to these regression algorithms is presented below. 1. Ordinary Least Squares (OLS) Regression Model  
The OLS regression model is one of most classic methods used for the spatial decomposition of demographic data. The principle of the OLS method is to find the best model by minimizing the sum of the squares of the residuals. For example, the demographic data can be fitted by using land use index, night light intensity, altitude, POI density, and road density. The regression model is built as follows:  
\[P_{i}^{pred}=\sum_{j=1}^{n}a_{j}L_{ij}+bN_{avg}+cE_{avg}\ +dR_{avg}\ +\sum_{k=1}^{n}e_{k}P_{ik}+ \text{g}, \tag{1}\]  
where \(P_{i}^{pred}\) denotes the predicted population of the \(i\)-th (\(i\) is from 1 to \(m\)) subdistrict; \(a_{j}\) denotes the coefficient of the population distribution for the \(j\)-th land use type; \(L_{ij}\) denotes the \(j\)-th land use type index of the \(i\)-th subdistrict; \(n\) is the total number of land use types; \(b\) is the coefficient of night light intensity; \(c\) denotes the coefficient of altitude; \(d\) represents the coefficient of roads density; \(N_{avg}\) represents the average night light intensity of each subdistrict; \(E_{avg}\) represents the average altitude of each subdistrict; \(R_{avg}\) represents the average road density of each subdistrict; \(e_{k}\) represents the coefficient for the \(k\)-th POI density index; \(P_{ik}\) represents the \(k\)-th POI type index of the \(i\)-th subdistrict; \(k\) represents the types of POI; and \(g\) is the constant term.