Which One Changes More? A Novel Radial Visualization for State Change Comparison

TL;DR

This paper introduces Intercept Graph, a radial ring-based visualization for comparing state changes across many data items by encoding change magnitude in the intercepted length of line segments between two circular axes. An interactive inner axis radius enables filtering of large changes and magnification of near-equal differences, addressing perceptual and scalability limitations of traditional grouped bar charts and slope graphs. The authors provide mathematical proofs linking line lengths to state-change magnitude, two usage scenarios (including NBA player ranking changes), metric evaluations (line-crossing and intensity ratio) against slope graphs, and a crowdsourced user study with 50 participants showing higher accuracy and comparable time costs. They also release an open-source implementation to facilitate adoption in real-world state-change analysis tasks across domains.

Abstract

It is common to compare state changes of multiple data items and identify which data items have changed more in various applications (e.g., annual GDP growth of different countries and daily increase of new COVID-19 cases in different regions). Grouped bar charts and slope graphs can visualize both state changes and their initial and final states of multiple data items, and are thus widely used for state change comparison. But they leverage implicit bar differences or line slopes to indicate state changes, which has been proven less effective for visual comparison. Both visualizations also suffer from visual scalability issues when an increasing number of data items need to be compared. This paper fills the research gap by proposing a novel radial visualization called Intercept Graph to facilitate visual comparison of multiple state changes. It consists of inner and outer axes, and leverages the lengths of line segments intercepted by the inner axis to explicitly encode the state changes. Users can interactively adjust the inner axis to filter large changes of their interest and magnify the difference of relatively-similar state changes, enhancing its visual scalability and comparison accuracy. We extensively evaluate the Intercept Graph in comparison with baseline methods through two usage scenarios, quantitative metric evaluations, and well-designed crowdsourcing user studies with 50 participants. Our results demonstrate the usefulness and effectiveness of the Intercept Graph.

Figures (7)

• Figure 1: Two visualizations for the comparison of the approval rate of democrats and republicans across the last 12 months. (Access date: 2022-6-19). Grouped bar charts (a) and slope graphs (b) cannot support a quick and accurate comparison of the approval rate difference in target months highlighted by green annotations.
• Figure 2: Visual design of Intercept Graph. (a) (b) Design alternatives of Intercept Graph. (c) The final design of Intercept Graph, which supports the smooth filtering and accurate comparison while mitigating the visual clutter of (a) and (b).
• Figure 3: The filtering and comparison features of Intercept Graph. (a) illustrated the filtering process of Intercept Graph. The number $n$ in the left half represents the number of the filtered items for each figure. "$+\Delta$" indicates the state changes to be filtered are generally positive. (b) shows the comparison feature of Intercept Graph. The figure on the left indicates Intercept Graph that the comparison of two pairs of data items' state changes is difficult to identify. As the inner axis shrinks inward, the relationships of each pair of data items are getting more and more apparent to identify.
• Figure 4: Comparative visualizations using a basketball dataset. (a) and (c) is Intercept Graph, where (a) shows the filtering of players with top 30 rising and dropping rankings, and (c) illustrates the accurate comparison of two pairs of players with close PPG ranking differences. (b) and (d) is the slope graph and grouped bar chart respectively, both driven by the basketball dataset which includes over 300 players.
• Figure 5: Metric evaluation of line crossing on randomly-generated datasets to compare the performance of proposed Intercept Graph and the baseline approach slope graphs. The error bars are 95% confidence intervals. Wilcoxon test statistics are reported at the top left of each figure. The p-values of each experiment are much less than 0.05, indicating a significant improvement in line crossing over the slope graphs.