# Human Clustering Based on Graph Embedding and Space Functions of Trajectory Stay Points on Campus
## 1 Introduction
Recently, deep learning technologies, including recurrent neural networks, convolutional neural networks, graph neural networks, and transformer-based models, together with attention mechanisms, have been introduced into trajectory data modeling, representation learning, trajectory clustering, and mobility simulation [6; 20; 21]. These technologies have been intensively applied to improve the effectiveness of trajectory similarity measurement and classification, which show advantages in extracting latent characteristic patterns, estimating travel time, and detecting anomalies, in addition to mobility generation. Most methodologies in available works adopt a data-driven trajectory approach to understand human mobility patterns and particular personal information. Most human movements are basically intentional movements with purposes [5; 9]. Spaces accommodating human movements offer relevant functions that meet the requirements of these purposes [9]. To better understand human behaviors, it is necessary to incorporate more semantic information of location and space, which accommodates required and desired activities. The built environment can act as a behavioral catalyst, suggesting that space functions may fundamentally shape mobility patterns in various disciplines across scales [12]. This perspective necessitates deeper integration of semantic space information with traditional trajectory analysis. Based on home location estimation [21], researchers validated the scaling law of visitation using mobile-phone data from multiple cities, which presented an inverse pattern of human travel distance relative to the frequency of trips from home. The findings supplement the gravity law and the radiation model of human mobility. Human mobility data generated in location-based social networks (LBSNs), such as those in FourSquare, empower researchers with semantically rich information in heterogeneous dimensions coupled with raw trajectory data of position and time [22]. Semantic information can be encoded into an attribute-embedding layer in neural network models, together with stay points in trajectories. In addition, user age groups [23] can be classified based on sparse spatial-temporal clustering and aggregation of trajectory data using machine learning algorithms [17]. In urban contexts, intensive interactions happen directly among human individuals who share similar spatio-temporal trajectories or indirectly among those who may use spaces with the same functions at different locations. As indicated above, most research mainly considers the former cases, adopting approaches using spatio-temporal similarities of trajectories. Specific functions of spaces accommodating trajectory stay points underpin human movements, enriching spatio-temporal patterns of corresponding trajectories. Recent advances in spatio-temporal visualization, as summarized in [PERSON] et al. 's systematic review of space-time cube operations [24], provide methodological foundations for the decoding of complex mobility patterns through 3D geo-visual analytics. The space function of trajectory stay points and the time that human individuals spend in spaces of specific functions reflect the purpose and drivers behind their behavior and corresponding activities. Recent advancements have shown the potential of incorporating space functions to enhance human clustering accuracy. Studies have incorporated types of buildings or areas that individuals visit to improve clustering performance for individuals with similar behavior patterns [25]. This consideration allows for a more comprehensive understanding of how individuals interact with different types of spaces. [PERSON] et al. categorized campus life trajectories into two types based on campus access points (APs) and inferred people's activities at different times according to the AP sets [25].