A quad-tree-based fast and adaptive Kernel Density Estimation algorithm for heat-map generation

Kernel Density Estimation (KDE) is a classic algorithm for analyzing the spatial distribution of point data, and widely applied in spatial humanities analysis. A heat-map permits intuitive visualization of spatial point patterns estimated by KDE without any overlapping. To achieve a suitable heat-map, KDE bandwidth parameter selection is critical. However, most generally applicable bandwidth selectors of KDE with relatively high accuracy encounter intensive computation issues that impede or limit the applications of KDE in big data era. To solve the complex computation problems, as well as make the bandwidths adaptively suitable for spatially heterogenous distributions, we propose a new Quad-tree-based Fast and Adaptive KDE (QFA-KDE) algorithm for heat-map generation. QFA-KDE captures the aggregation patterns of input point data through a quad-tree-based spatial segmentation function. Different bandwidths are adaptively calculated for locations in different grids calculated by the segmentation function; and density is estimated using the calculated adaptive bandwidths. In experiments, through comparisons with three mostly used KDE methods, we quantitatively evaluate the performance of the proposed method in terms of correctness, computation efficiency and visual effects. Experimental results demonstrate the power of the proposed method in computation efficiency and heat-map visual effects while guaranteeing a relatively high accuracy.