A spatial cluster of trajectories refers to objects that follow similar paths, revealing shared movement trends and aiding in anomaly detection. However, detecting clusters in trajectory data becomes challenging when the cluster-to-noise density ratio (CNDR) is low. For example, clusters in free-range sheep movements are easily seen due to their group behaviour, whereas the diversity of human movement introduces significant noise, making clustering difficult. The L-function, widely used for clustering detection in various data types (e.g. point or OD flow data), captures aggregation changes across scales without relying on predefined thresholds, offering potential for low CNDR trajectory data. Thus, we define a trajectory space to derive the Trajectory L (TL)-function for multipoint trajectories. Then we use the second derivative of the TL-function and the local TL-function to identify cluster sizes and extract clusters. Inflection points in the second derivatives enable the detection of subtle changes in aggregation, allowing for precise and sensitive cluster identification. Simulation experiments show that our method outperforms four state-of-the-art approaches in detecting clusters under low CNDR conditions while avoiding parameter dependency. We validated the generality and robustness of our method using both taxi GPS trajectories and mobile phone signalling trajectories. Furthermore, our work lays a rigorous and extensible foundation for the future formulation of spatiotemporal statistical frameworks tailored to trajectory data.

In urban regions, individuals predominantly spend their time indoors. Accurately identifying these indoor states is essential for many fields, such as public health and urban planning. Existing methods generally rely on sensors placed at specific locations or on volunteers’ mobile phones, limiting their applicability to those locations and a fraction of the population. To overcome these limitations, we propose a novel framework that leverages cellular signaling data—providing extensive spatio-temporal and population-wide coverage—to identify individuals’ indoor states comprehensively. We extract three types of features: interaction between individuals’ mobile phones and cells, individuals’ moving and stationary, and environmental context. Using these features, we apply three machine learning models—CatBoost, Random Forest (RF) and Support Vector Machine (SVM)—along with an interpretable machine learning model, Associative Tree (AT), to identify the indoor states. Evaluation with a ground truth dataset shows that CatBoost outperforms the other models, with an F1 score of 97.21% in quantifying the time individuals spend indoors. To our knowledge, this is the first study to identify the indoor states of individuals using cellular signaling data. We argue that this study can contribute to advancements in areas such as public health and urban planning.

In spatial point data, a hotspot is defined as a group of points with a significantly higher density within an arbitrarily shaped area. Among existing hotspot identification methods, spatial scan statistic, known for its simple mechanism in locating hotspots, has been extensively studied and applied in various fields. However, existing methods rely on pre-defined scanning window shapes, e.g. generic geometries like circles or pre-divided regions, like administrative divisions, and thereby may not accurately capture the irregular shapes of hotspots. This study enhances the spatial scan statistic by introducing a tightened window, which is defined as the window tightened to align with the hotspot’s shape. In our method, without the necessity of outlining the exact geometry, the area of the tightened window, estimated using the nearest distance statistics, is used for calculating the objective function. Experiments with simulated data demonstrate that our method outperforms existing methods in terms of testing hotspots’ significance, identifying arbitrarily shaped hotspots, estimating hotspots’ spatial extent, and reducing subjectivity in parameter selection. An empirical study using taxi pick-up point data shows our method can identify regions with high taxi demand and potential traffic congestion, including subway exits and commercial streets.

The mobility of scientists, manifested by movements to new academic institutions, grows with globalization and plays a crucial role in individual careers, institutional productivity, and knowledge dissemination. Current research on scientists’ mobility focuses on aggregated levels such as inter-country mobility, with little attention paid to fine-grained institutional level, leading to a simplified spatial portrayal of the mobility. To fill the gap, we take scientists in geography as examples, and reconstructed their dynamic mobility network among institutions from 1970 to 2020 based on massive literature metadata. Our findings reveal the spatial mobility pattern that is now dominated by North America, Western and Northern Europe, East Asia, and Oceania, with the trend of intensification, multipolarity, and inequality over time. Specifically, the mobility network exhibits clear community structure largely constrained by spatial proximity and national borders. We also uncovered a universal downward mobility pattern embedded in the hierarchical structure. Our quantitative analysis further suggest that mobility is facilitated by multiple realities, including spatial, cultural, and scientific proximity, institutional rankings and national economic levels, cooperation, and visa-free policies, with varying dynamics. These results contribute to spatiotemporal insights into the mechanisms of scientific development in theory, and the basis for talent policymaking in practice.

A geographical flow (hereafter flow) is defined as a movement between locations at two different times. A group of spatiotemporal flows can be viewed as a cluster if their origins and destinations are both spatiotemporally concentrated. Identifying spatiotemporal flow clusters may help reveal underlying spatiotemporal mobility trends or intensive relationships between regions. Despite recent advances in flow clustering methods, most only consider spatial attributes and ignore temporal information, and may fail to differentiate space-close but time-separated clusters. To this end, we derive global and local versions of the Spatiotemporal Flow L-function, extended from the classical L-function for points, and thereby construct a clustering method. First, the global version is utilized to check whether flow data contain clusters and estimate the spatial and temporal scales of the clusters. The local version is then employed to extract the clusters with the estimated scales. Experiments of simulated data demonstrate that our method outperforms three state-of-the-art methods in identifying spatiotemporal flow clusters with arbitrary shapes and different densities and reducing subjectivity in the parameter selection process. A case study with taxi data shows that our method reveals residents’ spatiotemporal moving patterns, including rush-hour commuting and whole-daytime transferring among railway stations.