A Bounded Measure for Estimating the Benefit of Visualization (Part II): Case Studies and Empirical Evaluation

Many visual representations, such as volume-rendered images and metro maps, feature a noticeable amount of information loss due to a variety of many-to-one mappings. At a glance, there seem to be numerous opportunities for viewers to misinterpret the data being visualized, hence, undermining the benefits of these visual representations. In practice, there is little doubt that these visual representations are useful. The recently-proposed information-theoretic measure for analyzing the cost-benefit ratio of visualization processes can explain such usefulness experienced in practice and postulate that the viewers' knowledge can reduce the potential distortion (e.g., misinterpretation) due to information loss. This suggests that viewers' knowledge can be estimated by comparing the potential distortion without any knowledge and the actual distortion with some knowledge. However, the existing cost-benefit measure consists of an unbounded divergence term, making the numerical measurements difficult to interpret. This is the second part of a two-part paper, which aims to improve the existing cost-benefit measure. Part I of the paper provided a theoretical discourse about the problem of unboundedness, reported a conceptual analysis of nine candidate divergence measures for resolving the problem, and eliminated three from further consideration. In this Part II, we describe two groups of case studies for evaluating the remaining six candidate measures empirically. In particular, we obtained instance data for (i) supporting the evaluation of the remaining candidate measures and (ii) demonstrating their applicability in practical scenarios for estimating the cost-benefit of visualization processes as well as the impact of human knowledge in the processes. The real world data about visualization provides practical evidence for evaluating the usability and intuitiveness of the candidate measures. The combination of the conceptual analysis in Part I and the empirical evaluation in this part allows us to select the most appropriate bounded divergence measure for improving the existing cost-benefit measure.