A Model of Information Visualization Interpretation

Since the groundbreaking work by Cleveland and McGill in 1984, studies have revealed the difficulties humans have extracting quantitative data from visualizations as simple as bar graphs. As a first step toward understanding this situation, this paper proposes a mathematical model of the interpretation effort of a bar graph using concepts drawn from eye tracking. First, three key areas of interest (AOIs) are identified, and fixations are modeled as random point clouds within the AOIs. Stochastic geometry is introduced via random triangles connecting fixations within the adjacent key visual regions. The so-called landmark methodology provides the basis for the probabilistic analysis of the constructed system. It is found that the random length of interest in a stochastic triangle has a noncentral chi distribution with a known mean. Unique to this model, in terms of previous landmark applications, is the inclusion of a correlation between fixations, which is justified by physiological studies of the eyes. This approach introduces several model parameters, such as the noncentrality parameter, variance of the fixation cloud, correlation between fixations, and a visualization scale. A detailed parametric analysis examining the dependence of the mean on these parameters is conducted. The paper ties this work to the visualization via a definition of the expected visual measurement error. An asymptotic analysis of the visual error is performed, and a simple expression is found to relate the expected visual measurement error to the key model parameters. From this expression, the influence these parameters have on a visualization’s interpretation is considered.