Direction-based multiple views on data

Abstract

In this paper, we propose the direction heat maps to visualize the spreads of points w.r.t. different observers in the Euclidean space. It is a new way to look points. Traditionally, the spread of points is unique because it depends on the absolute coordinates of points w.r.t. the zero point. However, considering the relative directions of the points, the spread varies if the observers are different. To visualize the multiple views on the same set of points, we design a pie-shaped heat map. On a direction range the more points are, on the heat map the darker the corresponding sector is. Supporting by the heat map, we can visually know whether the points spread over evenly around or the points scatter only in small direction ranges. The heat map can be widely used in many decision-making applications where the tasks are direction sensitive. Typically, in bicycle sharing applications, the heat map can tell a user the general spread of the available bikes around, and the user may choose to walk on the deep coloured direction to meet more bikes. To generate the heat map, we propose the direction profile to store the direction intervals associated with the number of points in the intervals. We design an algorithm to build the direction profile incrementally. To measure a spread, we define the direction-based centrality which is a statistic value to reflect the uniform degree of the spread. The lower the centrality is, the more evenly the points spread. The observer with the minimum centrality is a direction-based center, while the observer with the maximum centrality is a direction-based edge. We design an algorithm to calculate the centralities. To find the center faster, we also design an algorithm to approximate the centralities. The experimental results show that the heat map can visualize different spreads effectively and the direction-based centralities can be calculated efficiently.