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

Min Chen,Mateu Sbert

doi:10.3390/e24020228

Min Chen, Mateu Sbert

Open Access

https://doi.org/10.3390/e24020228

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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.

Highlights

IntroductionIt seems rather intuitive that visualization should be accurate, different data values should be visually encoded differently, and visual distortion should be disallowed
As this paper focuses on the theoretical discourse and conceptual evaluation, we use a highly abstracted version of this example to introduce the relevant information-theoretic notations and elaborate the problem statement addressed by this paper
We have considered the need to improve the mathematical formulation of an information-theoretic measure for analyzing the cost–benefit of visualization as well as other processes in a data intelligence workflow [1]

Summary

Introduction

It seems rather intuitive that visualization should be accurate, different data values should be visually encoded differently, and visual distortion should be disallowed. When we closely examine most (if not all) visualization images, we can notice that inaccuracy is ubiquitous. In volume visualization, when a pixel is used to depict a set of voxels along a ray, many different sets of voxel values may result in the same pixel color. A variety of complex geographical paths may be distorted and depicted as a straight line. Since there is little doubt that volume visualization and metro maps are useful, some “inaccurate” visualization must be beneficial

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Conclusion