# Detecting Urban Mobility Structure and Learning Functional Distribution with Multi-Scale Features
## 1 Introduction
For example, deep clustering [18] and graph embedding [19], with their powerful feature extraction capabilities, have shown unique advantages in handling large-scale and complex urban data. Compared to traditional methods, data-driven approaches not only effectively handle large-scale data but also uncover more detailed and comprehensive urban mobility structure information. As a result, these methods have garnered widespread attention from researchers in recent years. The urban mobility structure is complex, encompassing both crowd activity features and spatial structural features. However, current data-driven methods for detecting urban community structures mainly focus on learning local crowd activity features through node proximity, while learning global spatial structural features presents significant challenges. At the same time, urban networks are scale-free networks, and traditional community division metrics such as modularity make it difficult to measure the quality of urban mobility structures, neglecting the key factor that crowd movement is a direct representation of urban functional demands [20]. To address these limitations, we proposed a city activity structure embedding method that considers multi-scale features. The proposed method uses road network data and crowd travel data to construct an urban spatial activity structure map and designs a multi-scale comparison method to learn both local crowd activity features and global spatial structure features, generating region embedding vectors for urban mobility structure detection. Based on this, the region embedding vectors are further used to introduce a correlation matrix to explicitly encode the functional synergy and competitive relationships of POIs, enabling the learning of urban functional distribution and establishing a nonlinear mapping relationship between crowd activities and urban functional distribution. Finally, by quantifying the balance between crowd activity and service coverage under different urban spatial functional distributions, the method provides multi-objective optimization decision support for planners to address the complex challenges in urban spatial planning. The main contributions are summarized as follows:  
1. A city activity structure embedding method considering multi-scale features is designed. Building upon the urban spatial mobility network, we designed a learning framework that incorporates both local node contrast and global activity structure contrast. Additionally, we introduced a batch decay factor to integrate the local node contrast loss with the global activity structure contrast loss, thereby significantly enhancing the performance of urban mobility structure detection;  
2. Functional distribution learning based on urban mobility structures is conducted. We introduced a correlation matrix to explicitly encode the functional synergy and competitive relationships of POIs, enabling urban functional distribution learning, constructing a nonlinear mapping relationship between crowd activity structures and urban functions, and thereby evaluating the quality of regional embedding vectors and the balance between crowd activities and functional coverage;  
3. Experiments in Haikou City have shown that our method can accurately detect the urban mobility structure and functional distribution. The analysis reveals that the functions of Haikou's central urban area are highly concentrated, with a clear tidal movement effect, while the suburban functions are relatively weak, and residents have a high level of dependence on the central urban area. In the process of urban development, it is important to optimize the functional layout of the central urban area, improve suburban functions, and promote the balanced development of urban space. The paper is organized as follows: Section 2 introduces the related work. Section 3 introduces the proposed method. Section 4 implements the method on the Haikou City dataset and compares it with baseline methods.