Towards general-purpose representation learning of polygonal geometries

Neural network representation learning for spatial data (e.g., points, polylines, polygons, and networks) is a common need geographic artificial intelligence (GeoAI) problems. In recent years, many advancements have been made in networks, whereas little progress has especially complex polygonal geometries. this work, we focus on developing general-purpose polygon encoding model, which can encode geometry (with or without holes, single multipolygons) into an embedding space. The result embeddings be leveraged directly (or finetuned) downstream tasks such as shape classification, relation prediction, building pattern cartographic generalization, so on. To achieve model generalizability guarantees, identify few desirable properties that the encoder should satisfy: loop origin invariance, trivial vertex part permutation topology awareness. We explore two different designs encoder: one derives all representations domain naturally capture local structures of polygons; other leverages spectral easily global polygons. For approach propose ResNet1D, 1D CNN-based encoder, uses circular padding to invariance simple develop NUFTspec based Non-Uniform Fourier Transformation (NUFT), satisfies desired properties. conduct experiments tasks: 1) classification commonly used MNIST dataset; 2) polygon-based prediction new datasets (DBSR-46K DBSR-cplx46K) constructed from OpenStreetMap DBpedia. Our results show ResNet1D outperform multiple existing baselines with significant margins. While suffers performance degradation after shape-invariance modifications, very robust these modifications due nature NUFT representation. able jointly consider parts multipolygon their relations during while recognize details are sometimes important classification. This points promising research direction combining representations.