Directed kernel density estimation (DKDE) for time series visualization

Abstract

The purpose of this article is to investigate the density calculation and representation of spatially and temporally highly dynamic point data sets. We suggest an approach to explore point patterns that have a temporal dimension and therefore introduce an incremental development of the traditional kernel density estimation processes. Based on a movement vector assigned to each moving point, we apply a directed (or tilted) kernel to calculate and visualize the density pattern. The resulting density map recognizes the dynamic behavior of the underlying data points. By applying a shade effect or contour lines, the areas with densely distributed moving points are characterized by directed ‘ripples’ or ‘waves’. This assists the visual analysis and prediction of ‘movement trends’ based on the dynamic points. In our case study, we apply this method to airplane movement data limited to two points in time and we thereby visualize the results for the study area over Germany.