Scalable Kernel Density Classification via Threshold-Based Pruning

Density estimation forms a critical component of many analytics tasks including outlier detection, visualization, and statistical testing. These tasks often seek to classify data into high and low-density regions of a probability distribution. Kernel Density Estimation (KDE) is a powerful technique for computing these densities, offering excellent statistical accuracy but quadratic total runtime. In this paper, we introduce a simple technique for improving the performance of using a KDE to classify points by their density (density classification). Our technique, thresholded kernel density classification (tKDC), applies threshold-based pruning to spatial index traversal to achieve asymptotic speedups over naive KDE, while maintaining accuracy guarantees. Instead of exactly computing each point's exact density for use in classification, tKDC iteratively computes density bounds and short-circuits density computation as soon as bounds are either higher or lower than the target classification threshold. On a wide range of dataset sizes and dimensions, tKDC demonstrates empirical speedups of up to 1000x over alternatives.