## 3 Method
### Spatial Relationships between Geographical Entities  
As POI data were unavailable for some buildings, it was difficult to determine their functionality based on POI data. Therefore, we used the spatial relationships among buildings, roads, and POIs to identify the functional types of buildings. The spatial relationships between entities include topological spatial relationships, orientation spatial relationships, metric spatial relationships, and similar spatial relationships [38; 39].  
1. Spatial relationship between POIs and buildings. The topological spatial relationship between POIs and buildings can be simply categorised into two cases. (i) The building contains a certain number of POI points within the building. These may be of the same or different types. The number and category of POIs can reflect the functions of the building. (ii) The building does not contain any POI points. This type of building cannot be identified directly from POI points, so further processing is required.
2. The spatial relationship between two buildings. Two spatial entities have a spatial similarity relationship between them. Buildings with the same function tend to have certain similarity, such as footprint size, shape, distance, and orientation. By analysing the spatial similarity index between buildings without POIs and buildings with a known function, buildings with the same functional type can be identified.
3. Spatial relationship between roads and buildings. When identifying building functions, it should be noted that buildings on different sides of a road may have completely different functions. Usually, the buildings in residential communities or  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Functional Type of Urban Building** & **First-Level POI Category** & **Second-Level POI Category** \\ \hline Residential (R) & Real estate, business housing & Housing development, dormitory, condominium, etc. \\ \hline Commercial(C) & \begin{tabular}{c} Shopping, finance, hotel, beauty, \\ automobile service, life service, leisure \\ and entertainment, cuisine \\ \end{tabular} & \begin{tabular}{c} Department store, supermarkets, star hotel, \\ express hotel, beauty salon, car sale and \\ maintenance, restaurant, cafe, dessert store, \\ photo studio, agency, internet cafe, theatre, \\ cinema, for-profit training institution, bank, \\ pharmacy, pet hospital, etc. \\ \end{tabular} \\ \hline Office (O) & Company, commercial building & Company, industrial park, business office, etc. \\ \hline Public service (S) & \
\begin{tabular}{c} Government organisation, science and \\ education and cultural services, \\ cultural media \\ \end{tabular} &
\begin{tabular}{c} Primary and secondary schools, news \\ publishing house, place of culture, museum, \\ medical care, government organisation, public \\ prosecution and law enforcement institution, \\ other governmental organisation, etc. \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 2: POIs corresponding to building type.  
industrial parks are relatively far from main roads, while commercial centres are in convenient locations. A road mesh is an area surrounded by urban roads [40]. The buildings contained in the same road mesh have a high degree of functional similarity. A road mesh and building containment relationship can be used to preliminarily screen buildings with the same function and assist in analysing their functional types.