Learning Perceptual Kernels for Visualization Design.

Visualization design can benefit from careful consideration of perception, as different assignments of visual encoding variables such as color, shape and size affect how viewers interpret data. In this work, we introduce perceptual kernels: distance ma- trices derived from aggregate perceptual judgments. Perceptual kernels represent perceptual differences between and within visual variables in a reusable form that is directly applicable to visualization evaluation and automated design. We report results from crowd- sourced experiments to estimate kernels for color, shape, size and combinations thereof. We analyze kernels estimated using five different judgment types—including Likert ratings among pairs, ordinal triplet comparisons, and manual spatial arrangement—and compare them to existing perceptual models. We derive recommendations for collecting perceptual similarities, and then demonstrate how the resulting kernels can be applied to automate visualization design decisions. Visual encoding decisions are central to visualization design. As view- ers' interpretation of data may shift across encodings, it is important to understand how choices of visual encoding variables such as color, shape, size—and their combinations—affect graphical perception. One way to evaluate these effects is to measure the perceived simi- larities(orconversely, distances) between visual variables. Webroadly refer to subjective measures of judged similarity as perceptual dis- tances. In this context, a perceptual kernel is the distance matrix of aggregated pairwise perceptual distances. These measures quantify the effects of alternative encodings and thereby help create visualiza- tions that better reflect structures in data. Figure 1a shows a perceptual kernel for a set of symbols; distances are visualized using grayscale values, with darker cells indicating higher similarity. The prominent clusters suggest that users will perceive similarities among shapes that may or may not mirror encoded data values. Perceptual kernels can also benefit automated visualization design. Typically, automated design methods (27) leverage an effectiveness ranking of visual encoding variables with respect to data types (nom- inal, ordinal, quantitative). Once a visual variable is chosen, these methods provide little guidance on how to best pair data values with visual elements, instead relying on default palettes for variables such as color and shape. Perceptual kernels provide a means for computing optimized assignments to visual variables whose perceived differences are congruent with underlying distances among data points. In short, perceptual kernels enable the direct application of empirical percep- tion data within visualization tools. In this work, we contribute the results of crowdsourced experiments to estimate perceptual kernels for visual encoding variables of shape, size, color and combinations thereof. There are alternative ways of eliciting judged similarities among visual variables. We compare a variety of judgment types: Likert ratings among pairs, ordinal triplet comparisons, and manual spatial arrangement. We also assess the re- sulting kernels via comparisons to existing perceptual models. Wefind that ordinal triplet matching judgments provide the most consistent re- sults, albeit with higher time and money costs than pairwise ratings or spatial arrangement. We then demonstrate how perceptual kernels can be applied to improve visualization design through automatic palette optimization and by providing distances for visual embedding (8) of data points into visual spaces.