## 1 Introduction  
As a geospatial data type, an areal settlement plays an important role in the field of geographic information systems (GIS), usually appearing as a basic element in map updating [1, 2], cartographic generalization [3, 4, 5], and so on. To improve the readability and quality of areal settlement data, it is necessary to classify the shape of the areal settlement. As an important attribute of areal settlement elements, shape conveys a greater amount of information in the representation of geographical entities than color, texture, [6], etc. The shape recognition methods that national and international experts use for areal settlement can be broadly divided into two aspects:  
1. Shape description and recognition of the two-dimensional surface area of an areal settlement, which is also divided into two parts. One is based on the description of the overall shape after gridding of the vectorial areal settlement. For example, the most straightforward way to describe the shape of a building is by constructing a description of the chain code [7], the shape context [8] descriptor, using the grid as the object. It also converts remotely sensed images into raster images, with wavelet descriptors based on raster data [9], or histogram statistics [10], both of which can provide a good description of image features. The other is the abstraction of areas within the areal settlement in special shapes instead. For example, the areal settlement is matched with a template in the shape of the alphabet [11, 12]. This method is effective for the recognition of an areal settlement or the division of a two-dimensional plane into multiple triangular surface areas [13, 14], a good way of describing global and local shape features. All of these methods partition the areal settlement into regular geometric shapes, However, the results are not satisfactory for describing some of the more concave, convex, or complex areal settlements. 2. Description of the shape of the contour of the 2D-surface-shaped areal settlement boundary line, quantifying the contour with some special descriptive methods to describe the contour, for example, construction of a measure of the similarity of points on different contours through shape contexts [2], construction of the chordal eigenmatrix of a contour [15], multiscale shape representation of plane curves based on contour curvature [16], rotation functions [17], and description of the contours of building polygons using several spatial indicators [18]. These methods have the advantage of being computationally intuitive, but the two-dimensional surface contour information is too redundant and does not extract key concave and convex information for the classification of areal settlement shapes. In recent years, deep learning has achieved excellent results in computer vision, natural language processing, and speech recognition [19; 20; 21]. Commonly used in the earth sciences to understand spatial processes and improve geographical insight, it is primarily combined with regular grid-like data to extract geometric features through convolutional neural networks. For example, convolutional neural networks combined with rasterized remote sensing images [22] are used to extract key information about important overpass structures or road intersections [23] or contour line data of one-dimensional trajectories are processed into regular raster-like data [24]. Both are prepared for the needs of neural networks for regular-like data. However, the data for convolutional neural networks are supposed to be regularized grid-like data and cannot be applied directly to some irregularly shaped data. For this reason, some scholars have proposed graph convolutional neural networks (GCNs) [25], which use graph structures to construct irregular data, combined with convolutional neural networks. For example, graph data structures are constructed to recognize the shapes of river system clusters [26].