For point clusters, the conflict and crowding of map symbols is an inevitable problem during the transition from large to small scales. The cartographic generalization involved in this problem as a spatial decision-making process is usually related to the analysis of spatial context, the choice of abstraction operators, and the judgment of the resulting data quality. The rules summarized by traditional generalization methods usually require manual setting of conditions or thresholds and sometimes encounter special cases that make it difficult to directly match certain rules or integrate different rules together. An alternative method is using a data-driven strategy under AI technology background to simulate cartographer behaviors through typical sample training, such as deep learning. The integration of cartography domain knowledge and deep learning is a better choice to settle generalization decisions. This study uses a combination of domain knowledge and a data-driven approach to introduce graph neural networks into point cluster generalization. First, we construct a virtual graph structure of point clusters using Delaunay triangulation, secondly, we extract spatial features, contextual features, and attributes of each point separately, and then propose a generalization model based on the TAGCN network. Finally, this model is trained with the manually generalized sample to realize the automatic point cluster generalization. The results demonstrate that the proposed model is valid and efficient for point cluster generalization and that this algorithm can better maintain various characteristics of the point cluster in both the local area and the overall map compared to other methods.

This paper proposes a model to quantify the multiscale representation of a polyline based on iterative head/tail breaks. A polyline is first transformed into a corresponding Fourier descriptor consisting of normalized Fourier-series-expansion coefficients. Then, the most significant finite components of the Fourier descriptor are selected and ranked to constitute the polyline constrained Fourier descriptor. Using Shannon’s information theory, information content of the constrained Fourier-descriptor components is defined. Next, head/tail breaks are introduced to iteratively divide the constrained Fourier descriptor into head and tail components according to the heavy-tailed distribution of information contents. Thus, simplified polylines are reconstructed using ordered heads generated from head/tail breaks. Finally, the radical law is introduced and applied to model multiscale polyline representation by quantifying the scale of each simplified polyline. Three experiments are designed and conducted to evaluate the proposed model. The results demonstrate that the proposed model is valid and efficient for quantifying multiscale polyline representation.

Geographic features in maps consist of a mixture of points, polylines, and polygons, generally including POIs, roads, buildings, and other geographic features. Due to the differing dimensionality of these various types of geographic data, traditional geometric similarity measurement methods that rely on a single type of feature are not applicable to mixed scenes. The traditional solution to this issue is to treat points as projections of polylines and polylines as projections of polygons. Through neural networks, projection matrices can be learned to convert points, polylines, and polygons into the same type of object, thereby enabling the use of single-scene geometric measurement methods (e.g., Graph Neural Networks) to solve the problem. However, the key challenge in using Graph Neural Networks for similarity measurement is learning the adjacency relationships between geometric features. It is evident that the adjacency relationships between different feature pairs, such as polyline–polygon, polyline–polyline, and polygon–polygon, require different approaches for measurement, and these diverse relationships cannot be captured by a simple GNN. Heterogeneous Graph Neural Networks (HGNNs) are suited to address this problem: different adjacency relationships between feature pairs can be learned using distinct embedded networks, the new node characteristics can be calculated through the information aggregation and propagation framework of HGNNs, and these new characteristics can be used for geometric similarity measurement. Finally, the effectiveness of the proposed method was verified through practical experiments.

1. Large language models (LLMs) have greatly promoted the information mining, integration, and application of numerous scientific fields (Dramsch et al. 2025). The success of LLMs stems from the tr...

One of the goals of map generalization is to achieve real-time visualization of massive entities while adapting to zoom-in/zoom-out conditions. Unlike traditional map generalization, this type of scaling operation does not simplify the data to produce a final result; it only outputs temporary visualization data. To meet the current visualization scale requirements, we insert a simplification algorithm prior to visualization to process the data. Taking point simplification as an example, this study proposes a novel massive point selection method and optimizes the entire algorithmic process, enabling the method to quickly and efficiently handle point selection for datasets ranging from tens of thousands to millions of points. The method employs a geometric construction, namely a Delaunay triangulation, is applied to discover the distribution characteristics with real-time efficiency. Initially, we construct the Delaunay triangulation of the point cluster. Subsequently, we calculate the mean distance of each point as the selection feature. Finally, we incorporate a ‘fixed point’ concept to rank and stabilize the points during the selection process. Experimental results indicate that our method not only achieves commendable performance in considering spatial structure, comparable to both traditional and state-of-the-art methods but also demonstrates significantly higher efficiency. This method can efficiently handle point selection for datasets ranging from tens of thousands to millions of points in a short time, thereby greatly enhancing the practicality of the algorithm in complex point selection scenarios.