Quantitative Methods for Uncertainty Visualization

Abstract

Uncertainty is ubiquitous in the data that we collect. Nevertheless, when users create visualizations of this data, it is frequently neglected. The reason for this is twofold: For one, many common algorithms cannot handle uncertain data. If this is the case, the only option is to omit information and solely consider the most likely realization of the data. The second reason is that uncertainty is difficult to communicate to the user, either due to the lack of suitable visual variables or because users lack literacy in understanding uncertainty and its underlying mathematical model: probability distributions. The following thesis proposes methods to alleviate some of these problems by tackling two research questions: "How can we communicate uncertainty with its statistical properties?" and "How to adapt visualization methods to uncertainty?" First, we discuss sources of uncertainty, how to model it by using probability distributions, and different approaches for propagating uncertainty. Then, we propose a novel treemap technique designed to show uncertainty information. Our method relaxes the requirement of covering the entire designated space that traditional techniques adhere to. We propose modulated sine waves as a quantitative encoding of uncertainty, yet our resulting method is flexible to work with various visual variables. Next, we investigate how to perform dimensionality reduction on uncertainty data. We identify two general approaches: Monte Carlo sampling and analytical methods. We apply the former to adapt stress-majorization for creating layouts of probabilistic graphs. While Monte Carlo methods can be applied to a wide range of problems, the resulting visualizations can be difficult to interpret. On the other hand, analytical approaches do not share this drawback but are only viable if the uncertainty information can be propagated analytically through the projection. We show how this can be done to arrive at an uncertainty-aware version of principal component analysis. Besides, the analytical approach allows us to understand the projection's sensitivity to uncertainty in the data. Together with a summary of the developed methods, this thesis concludes with potential directions for future research. For this, we discuss Bayesian methods and their potential applications for handling uncertainty in visualization. Furthermore, we propose stippling, a form of visual abstraction, as a new way to visualize uncertainty in scalar fields.