SHIELD: Spatial Hierarchical Indexing,  Evaluation, and Linear Dynamics for Big Data Mining and Pattern Analysis

Managing large, high-dimensional spatial datasets is essential for emerging applications such as autonomous navigation, smart cities, and geospatial simulation. Traditional data reduction techniques often struggle to scale effectively while preserving the spatial relationships essential for advanced spatial reasoning tasks such as object detection. Depending on the dataset's characteristics, approaches such as downsampling, inpainting, or adaptive sampling—which we define as a process that dynamically combines the two—may be most effective. This paper introduces Spatial Hierarchical Indexing, Evaluation, and Linear Dynamics (SHIELD), a novel and lightweight framework designed for the adaptive sampling of large, high-dimensional spatial datasets. SHIELD enhances big data mining and pattern analysis by effectively performing significant data reductions similar to the Hierarchical Simplification approach while uniquely enabling inpainting at minimal overhead. One of its key innovations is TerTree, a ternary spatial partitioning counterpart to QuadTree. This structure allows for the identification of linear relationships and their extraction as vectors through a process we refer to as Linear Dynamics. We demonstrate that these vectors can be used to achieve cheap, high-quality inpainting. Our evaluation of SHIELD on an extensive, real-world LIDAR point cloud dataset shows it outperforms four popular lightweight downsampling methods. SHIELD is computationally competitive while uniquely facilitating inpainting and achieves balanced density preservation across diverse sample spaces of semantic interest.