Random Affine Transformation Feature Representation Learning for Fast Polygon Retrieval

Despite the advance of representation learning (RL) of image and text data, it is a challenging task to obtain a general-purpose representation of vector-based spatial data (e.g., point, polyline, and polygon) that fulfills domain-specific prerequisites in downstream spatial analysis. Towards filling this gap, we put focus on the first step of revisiting a classic computational geometry task, namely the polygon retrieval, with a modern RL approach. In this paper, we propose a novel representation learning method for polygon data, namely Random Affine Transformation Features (RATFs). Inspired by Random Fourier Features, RATFs represent polygons on the plane into vector embeddings in the high-dimensional space using the basis of random anchor polygons, allowing us to transform complex, non-batch-wise computations between polygons such as Hausdorff distance into simple, batch-wise inner products. Experiments demonstrate that by using a naive 3-layer feed-forward network, our RATFs-based neural polygon embeddings are able to retrieve similar polygons from the corpus 100,000 times faster than computing Hausdorff distances at inferencing and achieve good retrieval quality. We aim to demonstrate the representational power of RATFs and leave the design and tuning of more advanced RATFs-based neural networks for future work.