# A Reputation Model of OSM Contributor Based on Semantic Similarity of Ontology Concepts
## 3 Methods
### Contributor's Evaluation Reputation
#### 3.3.4 Topological Similarity of Object Version  
Topology is used mainly to describe the context of spatial changes between features and their adjacent versions. When both geometric changes and topology changes are considered, the spatial changes between object versions can be described more comprehensively. If the geometric characteristics of the object change, this may affect its spatial position, and then its topology will also change. For example, as shown in Figure 5, the two object versions \(A_{i}\) and \(B_{i}\) are close in space and overlap in topology, but when the geometric characteristics of the object version \(B_{i+1}\) change, its object versions \(A_{i+1}\) and \(B_{i+1}\) change from overlap to disjoint in topology.  
In the OSM platform, modifications of geographical objects always occur in the same type of objects, such as line or area objects. The most important topological relationships between two area objects are the overlap, disjoint, meet, and equal, etc. This study calculates mainly the topological similarity between different versions of a same object. The area overlap rate can quantify the topological relationship between versions, to a certain extent. Therefore, this study considers only the area overlap rate as a measurement of topological  
Figure 4: Polysemy lines expressed by the turning function.  
Figure 5: Graph of geometric changes affect topological diagrams.  
similarity. If it is a line object, we set a buffer around the line object, and the area overlap rate of the buffer is calculated, taking the centroid distance and area size between two adjacent versions of objects as the influencing factors of the area overlap rate. If the centroid positions of the two version objects are \(A(Lat_{A},Lon_{A})\) and \(B(Lat_{B},Lon_{B})\), respectively, the distance \(L_{A,B}\) between the two centroids is:  
\[L_{A,B}=2R*arcsin\left(\sqrt{sin^{2}\left(\frac{\text{Lat}_{A}-\text{Lat}_{B}}{ 2}\right)+\text{cos}(\text{Lat}_{A})*\text{cos}(\text{Lat}_{B})*sin^{2}\left( \frac{\text{Lon}_{A}-\text{Lon}_{B}}{2}\right)}\right) \tag{7}\]  
where \(R\) is the radius of the earth, approximately 6400 km, \(\text{Lat}_{A}\) is the latitude of centroids \(A\), \(\text{Lon}_{A}\) is the longitude of centroids \(A\), \(\text{Lat}_{B}\) is the latitude of centroids \(B\), and \(\text{Lon}_{B}\) is the longitude of centroids \(B\). In addition to the centroid distance, the area size is also used as a measure of the area overlap rate and mainly considers the overlap of the object area between two adjacent versions. The specific calculation method is as follows [49]:  
\[Sim_{topology}=\frac{Area_{a\cap b}}{Area_{max}(Area_{a},Area_{b})} \tag{8}\]  
where \(Area_{a\cap b}\) is the size of the intersection area between version \(a\) and version \(b\), and \(Area_{max}(Area_{a},Area_{b})\) is the maximum area between version \(a\) and version \(b\). The factors that affect the single evaluation value include semantic similarity, geometric similarity, and topological similarity, based on ontology concept. These three factors are important indicators of data quality contributed by contributors. The calculation method of one-time evaluation \(R_{c}(u)\) is:  
\[R_{c}(u)=\frac{Sim_{semantic}+Sim_{shape}+Sim_{topology}}{3} \tag{9}\]  
The one-time evaluation is a single evaluation for an object contributed by a user, but OSM users will contribute multiple object data, and in this case, users will be evaluated many times, so evaluation reputation is the accumulation of a single evaluation process. For example, the evaluation times of a user is \(m\), the evaluation reputation \(R_{e}(u)\) of the contributor is calculated as follows [32]:  
\[R_{e}(u)=\sum_{i=1}^{m}\frac{R_{c}(u)}{m} \tag{10}\]