Although Mobility Data Analysis (MDA) has been explored for a long time, it still lags behind advancements in other fields. A common issue in MDA is the lack of methods’ standardization and reusability. On the other hand, for instance, in time series analysis, the existing methods are typically general-purpose, and it is possible to apply them across diverse datasets and applications without extensive customization. Still, in MDA, most contributions are ad-hoc and designed to address specific research questions, which limits their generalizability and reusability. Recently, some researchers explored the application of shapelet transform to trajectory data, i.e., extracting discriminatory sub-trajectories from training data to be used as classification features. Unlike current MDA methods, this line of research eliminates the need for feature engineering, greatly improving its ability to generalize. While shapelets on mobility data have shown state-of-the-art performance on public classification datasets, it is still not clear why they work. Are these subtrajectories merely proxies for geographic location, or do they also capture motion dynamics? We empirically show that shapelet-based approaches are a viable alternative to classical methods and flexible enough to solve MDA tasks related solely to trajectory shape, solely to movement dynamics, and those related to both. Additionally, we investigate the problem of Geographic Transferability, showing that such approaches offer a promising starting point for tackling this challenge.

Abstract Geometric shape classification of vector polygons remains a challenging task in spatial analysis. Previous studies have primarily focused on deep learning approaches for rasterized vector polygons, while the study of discrete polygon representations and corresponding learning methods remains underexplored. In this study, we investigate a graph-based representation of vector polygons and propose a simple graph message-passing framework, PolyMP, along with its densely self-connected variant, PolyMP-DSC, to learn more expressive and robust latent representations of polygons. This framework hierarchically captures self-looped graph information and learns geometric-invariant features for polygon shape classification. Through extensive experiments, we demonstrate that combining a permutation-invariant graph message-passing neural network with a densely self-connected mechanism achieves robust performance on benchmark datasets, including synthetic glyphs and real-world building footprints, outperforming several baseline methods. Our findings indicate that PolyMP and PolyMP-DSC effectively capture expressive geometric features that remain invariant under common transformations, such as translation, rotation, scaling, and shearing, while also being robust to trivial vertex removals. Furthermore, we highlight the strong generalization ability of the proposed approach, enabling the transfer of learned geometric features from synthetic glyph polygons to real-world building footprints.

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