The rapid evolution of cities has brought new challenges to urban planning and management. The accurate evaluation of urban functional structure and mixed use is critical, especially at a fine scale such as by blocks. The composition and mixing of urban spatial functions calculated by remote sensing and statistics are non-quantitative and undetailed. The text topic models are often applied to process text data, but are rarely used to mine semantic information in quantitative data. Therefore, this paper attempts to carry out research on the recognition of urban functions and mixed use using a text topic generation model based on resident mobile data. First, the area within Wuhan Third Ring Road was divided into 2451 units at a grid size of 500 m × 500 m. The histogram-latent Dirichlet allocation (H-LDA) and information entropy were applied to assign different grid units to correct the functional topics and topic information entropy (TIE). Second, the functional categories of different analysis units were calculated using the point of interest (POI), frequency density (FD) and category proportion (CP) indicators, while the functional information entropy (FIE) based on the POI was calculated. Then, the urban functions and mixtures identified by the two kinds of data were compared and analyzed. Finally, referring to the geographic information in streetscape map and applying correlation analysis, the function and mixing results obtained from the experiment were verified. Studies have shown that the H-LDA model can identify bridges, which the POI data have shown is challenging to identify without attributes such as length. The function recognition accuracy of the H-LDA model is 89.3%, which is higher than K-means algorithm and Word2vec models. The correlation coefficient between FIE and TIE is 0.587, indicating that both are highly correlated. These explain the accuracy and rationality of identifying city functions and mixtures based on the H-LDA model. The H-LDA model can be applied to functional computing and fine-scale urban mixed function planning.

The supply–demand relationship of urban public service facilities is the key to measuring a city’s service level and quality, and a balanced supply–demand relationship is an important indicator that reflects the optimal allocation of resources. To address the problem presented by the unbalanced distribution of educational resources, this paper proposes a dynamic Voronoi diagram algorithm with conditional constraints (CCDV). The CCDV method uses the Voronoi diagram to divide the plane so that the distance from any position in each polygon to the point is shorter than the distance from the polygon to the other points. In addition, it can overcome the disadvantage presented by the Voronoi diagram’s inability to use the nonspatial attributes of the point set to precisely constrain the boundary range; the CCDV method can dynamically plan and allocate according to the school’s capacity and the number of students in the coverage area to maintain a balance between supply and demand and achieve the optimal distribution effect. By taking the division of school districts in the Bao’an District, Shenzhen, as an example, the method is used to obtain a school district that matches the capacity of each school, and the relative error between supply and demand fluctuates only from −0.1~0.15. According to the spatial distribution relationship between schools and residential areas in the division results, the schools in the Bao’an District currently have an unbalanced distribution in some areas. A comparison with the existing school district division results shows that the school district division method proposed in this paper has advantages. Through a comprehensive analysis of the accessibility of public facilities and of the balance of supply and demand, it is shown that school districts based on the CCDV method can provide a reference for the optimal layout of schools and school districts.

Affinity propagation (AP) is a clustering algorithm for point data used in image recognition that can be used to solve various problems, such as initial class representative point selection, large-scale sparse matrix calculations, and large-scale data with fewer parameter settings. However, the AP clustering algorithm does not consider spatiotemporal information and multiple thematic attributes simultaneously, which leads to poor performance in discovering patterns from massive spatiotemporal points (e.g., trajectory points). To resolve this issue, a multidimensional spatiotemporal affinity propagation (MDST-AP) algorithm is proposed in this study. First, the similarity of spatial and nonspatial attributes is measured in Gaussian kernel space instead of Euclidean space, which helps address the multidimensional linear inseparability problem. Then, the Davies-Bouldin (DB) index is applied to optimize the parameter value of the MDST-AP algorithm, which is applied to analyze road congestion in Beijing via taxi trajectories. Experiments on different datasets and algorithms indicated that the MDST-AP algorithm can process multidimensional spatiotemporal data points faster and more effectively.