Kernel functions support a broad range of applications that require tasks like density estimation, classification, regression or outlier detection. For these tasks, a common online operation is to compute the weighted aggregation of kernel function values with respect to a set of points. However, scalable aggregation methods are still unknown for typical kernel functions (e.g., Gaussian kernel, polynomial kernel, sigmoid kernel and additive kernels) and weighting schemes. In this paper, we propose a novel and effective bounding technique, by leveraging index structures, to speed up the computation of kernel aggregation. In addition, we extend our technique to additive kernel functions, including$\chi ^2$, intersection, JS and Hellinger kernels, which are widely used in different communities, e.g., computer vision, medical science, Geoscience etc. To handle the additive kernel functions, we further develop the novel and effective bound functions to efficiently evaluate the kernel aggregation. Experimental studies on many real datasets reveal that our proposed solution KARL achieves at least one order of magnitude speedup over the state-of-the-art for different types of kernel functions.

Kernel density visualization (KDV) is a commonly used visualization tool for many spatial analysis tasks, including disease outbreak detection, crime hotspot detection, and traffic accident hotspot detection. Although the most popular geographical information systems, e.g., QGIS, and ArcGIS, can also support this operation, these solutions are not scalable to generate a single KDV for datasets with million-scale data points, let alone to support exploratory operations (e.g., zoom in, zoom out, and panning operations) with KDV in near real-time (< 5 sec). In this demonstration, we develop a near real-time visualization system, called KDV-Explorer, that is built on top of our prior study on the efficient kernel density computation. Participants will be invited to conduct some kernel density analysis on three large-scale datasets (up to 1.3 million data points), including the traffic accident dataset, crime dataset and COVID-19 dataset. We will also compare the performance of our solution and the solutions in QGIS and ArcGIS.