## 2 Materials and Methods
### Data
#### 2.2.2 POI Data
The formula for the concept-coincidence factor \(IF_{\mathrm{coi}}\) is as follows:  
\[IF_{\mathrm{coi}}=\frac{\mathrm{count}(\mathrm{Up}(C_{1})\cap(\mathrm{Up}(C_{ 2})))}{\mathrm{max}(ConDep(C_{1}),ConDep(C_{2}))} \tag{4}\]  
where \(\mathrm{count}(\mathrm{Up}(C_{1})\cap(\mathrm{Up}(C_{2})))\) represents the number of common ancestor nodes contained in the concept nodes \(C_{1}\) and \(C_{2}\), and \(\mathrm{max}(ConDep(C_{1}),ConDep(C_{2}))\) represents the maximum value of the level depth in the concept nodes \(C_{1}\) and \(C_{2}\). If the number of common ancestor nodes of two concept nodes is greater, the degree of overlap of their concepts is higher, and the similarity is greater. Five semantic relationships were considered in the research: Synonym, Induced-By, Inheritance (Is-a), Part-of, and Coordinate-term-of. The formula of the semantic-relationship influence factor \(IF_{Rel}\) is as follows:  
\[IF_{Rel}=\frac{\sum_{i=1}^{N_{S}}Value(C_{i},\ F_{i})}{N_{S}} \tag{5}\]\[Value(C_{i},\ F_{i})=\left\{ \begin{array}{cl}&1&Synonym(C_{i},\ F_{i})\\ &\frac{1}{2}&Induced-By(C_{i},\ F_{i})\\ &\frac{1}{3}&Is-a(C_{i},\ F_{i})\\ &\frac{1}{3}&Part-of(C_{i},\ F_{i})\\ &\frac{1}{4}&Coordinate-term-of(C_{i},\ F_{i})\end{array} \right.\]  
where \(N_{S}\) represents the number of the shortest paths between concepts \(C_{1}\) and \(C_{2},\ C_{i}\) represents the \(i\)-th concept node on the shortest path, and \(F_{i}\) represents the parent concept of \(C_{i}\). Value \((C_{i},\ F_{i})\) represents the weight of the directed edge between concept node \(C_{i}\) and its parent concept node \(F_{i}\). Combining the above five influencing factors, the formula for calculating the concept of semantic similarity between concepts \(C_{1}\) and \(C_{2}\) sim\((C_{1},C_{2})\) is as follows:  
\[\text{sim}(C_{1},C_{2})=\text{f}_{1}\times\text{IF}_{\text{Dis}}+\text{f}_{2} \times\text{IF}_{\text{Den}}+\text{f}_{3}\times\text{IF}_{\text{Dep}}+\text{ f}_{4}\times\text{IF}_{\text{coi}}+\text{f}_{5}\times\text{IF}_{\text{Rel}} \tag{6}\]  
where f\({}_{1}\), f\({}_{2}\), f\({}_{3}\), f\({}_{4}\), and f\({}_{5}\) are the adjustment factors. In order to obtain the topic semantic-weight vector, topic concept \(C\) was first determined, and then the concept of semantic similarity between each topic word in topic vector TK and topic concept \(C\) was calculated according to Formula (6), and the topic semantic-weight vector is WTK \(\left\{\text{wtk}_{1},\ \text{wtk}_{2},\ \ldots\text{wtk}_{i}\ldots,\ \text{wtk}_{n}\right\}\). The WTK calculation formula is as follows:  
\[\text{WTK}=(\text{sim}(C,\text{tk}_{1}),\text{sim}(C,\text{tk}_{2}),\ldots.\ldots,\text{sim}(C,\text{tk}_{n})) \tag{7}\]  
where wtk\({}_{i}\) represents the topic semantic-weight of the \(i\)-th topic word in the topic vector, that is, the semantic similarity value between topic concept \(C\) and topic word tk. The POI data on the AutoNavi map, using the Mars coordinate system, were used in the research. To facilitate the subsequent data analysis, a conversion algorithm was used to convert the Martian coordinate system to the WGS84 coordinate system during the data visualization. Then, the satellite image layer of the Gaode Map [76] was used to locate the 9368 residential areas in Wuhan, manually identify and confirm the spatial layout of the residential areas, and finally aggregate the 8330 residential areas used in the study.