A Bounded Measure for Estimating the Benefit of Visualization (Part I): Theoretical Discourse and Conceptual Evaluation

Abstract

Information theory can be used to analyze the cost–benefit of visualization processes. However, the current measure of benefit contains an unbounded term that is neither easy to estimate nor intuitive to interpret. In this work, we propose to revise the existing cost–benefit measure by replacing the unbounded term with a bounded one. We examine a number of bounded measures that include the Jenson–Shannon divergence, its square root, and a new divergence measure formulated as part of this work. We describe the rationale for proposing a new divergence measure. In the first part of this paper, we focus on the conceptual analysis of the mathematical properties of these candidate measures. We use visualization to support the multi-criteria comparison, narrowing the search down to several options with better mathematical properties. The theoretical discourse and conceptual evaluation in this part provides the basis for further data-driven evaluation based on synthetic and experimental case studies that are reported in the second part of this paper.

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

“…This two-part paper is concerned with information-theoretic measures for quantifying aspects of visualization, such as benefit, knowledge, and potential misinterpretation. The first part [ 4 ] focuses its review on previous information-theoretic work in visualization. In this section, we focus our review on previous measurement work in visualization.…”

“…This cost–benefit ratio was described and discussed in the first part of the paper [ 4 ]. Appendix A provides a more detailed explanation of this measure in the context of visualization, while Appendix B explains in detail how tasks and users are considered by this measure in the abstract.…”

“…In the first part of this paper [ 4 ], Chen and Sbert showed that, conceptually, it is the unboundedness that is not consistent with a conceptual interpretation of KL-divergence for measuring the inefficiency of a code (alphabet) that has a finite number of codewords (letters). They proposed to find a suitable bounded divergence measure to replace the term in Equation ( 2 ).…”

“…However, this measure consists of an unbounded divergence term, making the numerical measurements difficult to interpret. In the first part of this paper [ 4 ], Chen and Sbert: Reviewed the related work that prepared for this cost–benefit measure, provided the measure with empirical evidence, and featured the application of the measure. Identified a shortcoming of using the Kullback–Leibler divergence (KL-divergence) in the cost–benefit measure and demonstrated the shortcoming using practical examples.…”

“…Readers are encouraged to consult the related reports on the cost–benefit analysis [ 5 ] and the Part I of this paper [ 4 ]. Nevertheless, this part of the paper is written in a self-contained manner.…”