# A Transformer-Based Approach for Efficient Geometric Feature Extraction from Vector Shape Data
## 1 Introduction  
Extracting various features of vector elements is crucial for advanced tasks, such as intelligent processing, analysis, mining, automated generalization, data matching and updating, and database derivation. Feature extraction for vector elements primarily focuses on line and polygon elements. Line elements commonly appear in trees or network structures such as rivers, road networks, and contour lines [1]. Polygon elements oftenmanifest as regular or irregular shapes, cluster structures, or nested formations, including buildings, farmlands, lakes, forests, residential areas, and urban planning zones [2]. Existing methods typically employ different machine learning algorithms to extract features for different types of line and polygon elements. For example, different algorithms have been used for buildings [3; 4; 5], lakes [6; 7; 8], roads [9; 10; 11], and rivers [12; 13; 14], which limits the general applicability of these approaches. Current research on vector elements encompasses tasks such as shape classification, pattern recognition, cartographic generalization, and answering geographical questions. The encoding and representation of shape features play a critical role in these tasks. For example, in shape classification tasks, [PERSON] and [PERSON] (2022) compared GraphNet with several deep learning-based methods, such as GraphNet, SeqNet, and PixelNet, and found that GraphNet outperformed traditional geometric methods in shape encoding [15]. [PERSON] et al. (2021) proposed the shape-tree principle, enhancing multiscale shape expression by reconstructing the organizational structure of geographical elements [16]. [PERSON] et al. (2023) demonstrated the potential of novel deep learning methods in geographic information systems by using a Siamese neural network to learn linear feature similarity metrics [3]. [PERSON] et al. (2023) combined Fast Fourier Transform and random forests to achieve efficient classification of homestead shapes, highlighting the synergy between traditional feature extraction and machine learning [17]. The Deep Graph Fourier Network proposed by [PERSON] et al. (2023) achieved high-precision recognition of building shapes through multilayer graph signal filtering, showcasing the application advantages of the graph signal processing theory [5]. Additionally, for pattern recognition tasks, [PERSON] et al. (2021) investigated the application of deep graph convolutional networks (GCNs) in automated road network selection, emphasizing that GCNs could effectively extract spatial features, surpass traditional methods, and reduce human intervention [18]. [PERSON] and [PERSON] (2023) emphasized the role of graph convolutional neural networks (GCNNs) in identifying the grid distribution patterns of buildings and improving accuracy by integrating geometric and structural features [19]. [PERSON] and [PERSON] (2022) introduced an unsupervised learning method for urban morphology abstraction using multiscale residual convolutional autoencoders (MRCAEs), offering flexibility and label independence in complex urban morphology classifications [20]. [PERSON] and [PERSON] (2022) proposed a graph deep learning method for urban building grouping, effectively capturing intra-group cohesion and inter-group separation through a graph Fourier transformation and feature integration [21]. Finally, [PERSON] et al. (2022) developed a graph convolutional network combining shape and semantic features for urban scene classification, achieving outstanding accuracy by utilizing neighborhood-supported spatial relationships [22]. In tasks involving cartographic generalization and geographic question answering, [PERSON] et al. (2019) evaluated U-net, Res-U-net, and GAN architectures and found that Res-U-net performs optimally across multiple map scales by encoding shape features and automating tasks, such as selection and aggregation, without explicitly defining interaction rules [23]. [PERSON] et al.