## 3 Method
### Validation of Results  
We randomly selected 957 buildings to validate the identification results. Producer accuracy (PA) and user accuracy (UA) were calculated for each building function type. The building identification result is shown in Table 4. Public service buildings and residential buildings have the highest identification precision, having both PA and UA of >90%. The PA and UA of mixed commercial and public service buildings and mixed residential and public service buildings are <70%, indicative of low identification precision. The PA of residential buildings, residential and commercial buildings, and complex functional buildings are lower than their UA. These types of buildings are underclassified at a high rate. The number of buildings identified is less than the actual number of buildings in the corresponding category. The PA of other types of buildings are higher than their UA, indicating that misclassification occurs more often than failed classification. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \begin{tabular}{c} **Functional** \\ **Type** \\ \end{tabular}  & **O** & **OS** & **S** & **C** & **CO** & **CS** & **R** & **RO** & **RS** & **RC** & **F** \\ \hline \begin{tabular}{c} **O** \\ **OS** \\ **S** \\ \end{tabular}  & \begin{tabular}{c} 30 \\ 1 \\ 1 \\ 2 \\ \end{tabular}  & \begin{tabular}{c} 1 \\ 1 \\ 1 \\ 2 \\ \end{tabular}  & \begin{tabular}{c} 2 \\ 1 \\ 1 \\ 2 \\ \end{tabular}  & \begin{tabular}{c} 1 \\ 1 \\ 2 \\ \end{tabular}  & \ \begin{tabular}{c} 3 \\ 1 \\ 2 \\ \end{tabular}  &
\begin{tabular}{c} 0 \\  
Kernel density based on POI [29] had the lowest precision in building function identification, with an F1 value of only 6.04%. The Tyson polygon area share method [33] had a higher recall rate of 94.79% but its accuracy was only 74.17%, indicating that it can easily misclassify buildings. The proposed method had the highest overall identification precision, with accuracy, recall and F1 values all >90%. Figure 5 compares the functional identification results of the proposed method and the kernel density method for the Langdong Farmers' Market in Nanning City. This market mainly includes retail, catering, hotels, chess and cards, and entertainment. From Figure 5a,b, it can be seen that there are multiple POIs in Nanning Langdong Farmers' Market, which are mainly commercial POIs. According to the proposed method, the buildings in Nanning Langdong Farmers' Market are identified as commercial buildings, as shown in Figure 5c, which is accurate. The kernel density method [29] incorrectly identified the market as having residential buildings due to the high number of residential POIs in the neighbourhood, as shown in Figure 5d. Figure 6 compares building functional identification by the proposed and kernel density methods at Nanning People's Hall. The People's Hall is the meeting place of the People's Congress and the office of the Standing Committee of the People's Congress. It is a place where political, diplomatic, and cultural activities are held. From Figure 6a,b, it can be seen that there are two POIs in the Nanning People's Hall building, both of which are public service POIs. According to the proposed method, the building is correctly identified as a public service building, as shown in Figure 6c. Because of the surrounding Nanning International Convention and Exhibition Center, Hangyang City and residential communities, the kernel density method [29] incorrectly identifies the Nanning People's Hall as having mixed residential and public service, office, and public service functions, as shown in Figure 6d.