Geographic knowledge graph representation learning requires generating the corresponding negative samples based on the positive ones. However, traditional negative sample generation algorithms suffer from high error rate and poor adaption to geographic knowledge graph. Aimming at this problem, a spatially constraint negative sample generation method was proposed by modifying the modeling of spatial relations. Then the method was applied to different knowledge graph representation learning models to explore its suitability in geographic knowledge graph embedding. Results show that the proposed method has a low error rate and is suitable for two common types of knowledge graph representation models. The spatially constraint negative sample generation method will improve the accuracy of geographic knowledge graph representation learning, which helps to advance geographical research.

Based on the three levels of mathematical statistics, topological network and geometric network, the accessibility measurements on public service facilities in existing studies are teased, and the fundamental principles, metrics, range of applicability, the advantage and disadvantage of these different measurements are reviewed. It is pointed out that current methodological task is to find the right balance between a measure that is theoretically and empirically sound and one that is sufficiently plain, and emergence of new data technologies provides a new direction for accessibility measurements.

With the purpose of analyzing the spatial distribution and fairness of public service facilities in Beijing, Gauss two-step floating catchment area method is applied to assess the accessibility within the Fifth Ring Road of Beijing in 5 dimensions, including education, healthcare, commerce, transportation, and culture leisure service, and the weighted composite accessibility is calculated. Then, hedonic price model is adopted to further analyze the impact of public service facilities accessibility on housing prices. It is found that the accessibility of public service facilities is unevenly distributed, and most resources are concentrated on certain district. The accessibility of education and healthcare service is significantly higher in the central urban area than that in other regions, and commerce accessibility in the eastern area is higher than that in the western. Transportation and culture leisure resources are relatively scattered. There is a significant positive impact of healthcare and transportation accessibility on housing price, a significant negative impact of commerce accessibility and no significant effect of education and culture leisure accessibility on housing price. The comprehensive accessibility is also proved to have a significant positive impact on housing price. These results provide support for urban planning, especially for the rational distribution of public service facilities.