  Geometric shape classification of vector polygons remains a non-trivial
learning task in spatial analysis. Previous studies mainly focus on devising
deep learning approaches for representation learning of rasterized vector
polygons, whereas the study of discrete representations of polygons and
subsequent deep learning approaches have not been fully investigated. In this
study, we investigate a graph representation of vector polygons and propose a
novel graph message-passing neural network (PolyMP) to learn the
geometric-invariant features for shape classification of polygons. Through
extensive experiments, we show that the graph representation of polygons
combined with a permutation-invariant graph message-passing neural network
achieves highly robust performances on benchmark datasets (i.e., synthetic
glyph and real-world building footprint datasets) as compared to baseline
methods. We demonstrate that the proposed graph-based PolyMP network enables
the learning of expressive geometric features invariant to geometric
transformations of polygons (i.e., translation, rotation, scaling and shearing)
and is robust to trivial vertex removals of polygons. We further show the
strong generalizability of PolyMP, which enables generalizing the learned
geometric features from the synthetic glyph polygons to the real-world building
footprints.
