More of what? Dissociating effects of conceptual and numeric mappings on interpreting colormap data visualizations.

In visual communication, people glean insights about patterns of data by observing visual representations of datasets. Colormap data visualizations ("colormaps") show patterns in datasets by mapping variations in color to variations in magnitude. When people interpret colormaps, they have expectations about how colors map to magnitude, and they are better at interpreting visualizations that align with those expectations. For example, they infer that darker colors map to larger quantities (dark-is-more bias) and colors that are higher on vertically oriented legends map to larger quantities (high-is-more bias). In previous studies, the notion of quantity was straightforward because more of the concept represented (conceptual magnitude) corresponded to larger numeric values (numeric magnitude). However, conceptual and numeric magnitude can conflict, such as using rank order to quantify health-smaller numbers correspond to greater health. Under conflicts, are inferred mappings formed based on the numeric level, the conceptual level, or a combination of both? We addressed this question across five experiments, spanning data domains: alien animals, antibiotic discovery, and public health. Across experiments, the high-is-more bias operated at the conceptual level: colormaps were easier to interpret when larger conceptual magnitude was represented higher on the legend, regardless of numeric magnitude. The dark-is-more bias tended to operate at the conceptual level, but numeric magnitude could interfere, or even dominate, if conceptual magnitude was less salient. These results elucidate factors influencing meanings inferred from visual features and emphasize the need to consider data meaning, not just numbers, when designing visualizations aimed to facilitate visual communication.

Red and blue states: dichotomized maps mislead and reduce perceived voting influence.

In the United States the color red has come to represent the Republican party, and blue the Democratic party, in maps of voting patterns. Here we test the hypothesis that voting maps dichotomized into red and blue states leads people to overestimate political polarization compared to maps in which states are represented with continuous gradations of color. We also tested whether any polarizing effect is due to partisan semantic associations with red and blue, or if alternative hues produce similar effects. In Study 1, participants estimated the hypothetical voting patterns of eight swing states on maps with dichotomous or continuous red/blue or orange/green color schemes. A continuous gradient mitigated the polarizing effects of red/blue maps on voting predictions. We also found that a novel hue pair, green/orange, decreased perceived polarization. Whether this effect was due to the novelty of the hues or the fact that the hues were not explicitly labeled "Democrat" and "Republican" was unclear. In Study 2, we explicitly assigned green/orange hues to the two parties. Participants viewed electoral maps depicting results from the 2020 presidential election and estimated the voting margins for a subset of states. We replicated the finding that continuous red/blue gradient reduced perceived polarization, but the novel hues did not reduce perceived polarization. Participants also expected their hypothetical vote to matter more when viewing maps with continuous color gradations. We conclude that the dichotomization of electoral maps (not the particular hues) increases perceived voting polarization and reduces a voter's expected influence on election outcomes.

Unifying Effects of Direct and Relational Associations for Visual Communication.

People have expectations about how colors map to concepts in visualizations, and they are better at interpreting visualizations that match their expectations. Traditionally, studies on these expectations (inferred mappings) distinguished distinct factors relevant for visualizations of categorical vs. continuous information. Studies on categorical information focused on direct associations (e.g., mangos are associated with yellows) whereas studies on continuous information focused on relational associations (e.g., darker colors map to larger quantities; dark-is-more bias). We unite these two areas within a single framework of assignment inference. Assignment inference is the process by which people infer mappings between perceptual features and concepts represented in encoding systems. Observers infer globally optimal assignments by maximizing the "merit," or "goodness," of each possible assignment. Previous work on assignment inference focused on visualizations of categorical information. We extend this approach to visualizations of continuous data by (a) broadening the notion of merit to include relational associations and (b) developing a method for combining multiple (sometimes conflicting) sources of merit to predict people's inferred mappings. We developed and tested our model on data from experiments in which participants interpreted colormap data visualizations, representing fictitious data about environmental concepts (sunshine, shade, wild fire, ocean water, glacial ice). We found both direct and relational associations contribute independently to inferred mappings. These results can be used to optimize visualization design to facilitate visual communication.

Context Matters: A Theory of Semantic Discriminability for Perceptual Encoding Systems.

People's associations between colors and concepts influence their ability to interpret the meanings of colors in information visualizations. Previous work has suggested such effects are limited to concepts that have strong, specific associations with colors. However, although a concept may not be strongly associated with any colors, its mapping can be disambiguated in the context of other concepts in an encoding system. We articulate this view in semantic discriminability theory, a general framework for understanding conditions determining when people can infer meaning from perceptual features. Semantic discriminability is the degree to which observers can infer a unique mapping between visual features and concepts. Semantic discriminability theory posits that the capacity for semantic discriminability for a set of concepts is constrained by the difference between the feature-concept association distributions across the concepts in the set. We define formal properties of this theory and test its implications in two experiments. The results show that the capacity to produce semantically discriminable colors for sets of concepts was indeed constrained by the statistical distance between color-concept association distributions (Experiment 1). Moreover, people could interpret meanings of colors in bar graphs insofar as the colors were semantically discriminable, even for concepts previously considered "non-colorable" (Experiment 2). The results suggest that colors are more robust for visual communication than previously thought.

A Holey Perspective on Venn Diagrams.

When interpreting the meanings of visual features in information visualizations, observers have expectations about how visual features map onto concepts (inferred mappings.) In this study, we examined whether aspects of inferred mappings that have been previously identified for colormap data visualizations generalize to a different type of visualization, Venn diagrams. Venn diagrams offer an interesting test case because empirical evidence about the nature of inferred mappings for colormaps suggests that established conventions for Venn diagrams are counterintuitive. Venn diagrams represent classes using overlapping circles and express logical relationships between those classes by shading out regions to encode the concept of non-existence, or none. We propose that people do not simply expect shading to signify non-existence, but rather they expect regions that appear as holes to signify non-existence (the hole hypothesis.) The appearance of a hole depends on perceptual properties in the diagram in relation to its background. Across three experiments, results supported the hole hypothesis, underscoring the importance of configural processing for interpreting the meanings of visual features in information visualizations.

Semantic Discriminability for Visual Communication.

To interpret information visualizations, observers must determine how visual features map onto concepts. First and foremost, this ability depends on perceptual discriminability; observers must be able to see the difference between different colors for those colors to communicate different meanings. However, the ability to interpret visualizations also depends on semantic discriminability, the degree to which observers can infer a unique mapping between visual features and concepts, based on the visual features and concepts alone (i.e., without help from verbal cues such as legends or labels). Previous evidence suggested that observers were better at interpreting encoding systems that maximized semantic discriminability (maximizing association strength between assigned colors and concepts while minimizing association strength between unassigned colors and concepts), compared to a system that only maximized color-concept association strength. However, increasing semantic discriminability also resulted in increased perceptual distance, so it is unclear which factor was responsible for improved performance. In the present study, we conducted two experiments that tested for independent effects of semantic distance and perceptual distance on semantic discriminability of bar graph data visualizations. Perceptual distance was large enough to ensure colors were more than just noticeably different. We found that increasing semantic distance improved performance, independent of variation in perceptual distance, and when these two factors were uncorrelated, responses were dominated by semantic distance. These results have implications for navigating trade-offs in color palette design optimization for visual communication.

The relation between color and spatial structure for interpreting colormap data visualizations.

Interpreting colormap visualizations requires determining how dimensions of color in visualizations map onto quantities in data. People have color-based biases that influence their interpretations of colormaps, such as a dark-is-more bias-darker colors map to larger quantities. Previous studies of color-based biases focused on colormaps with weak data spatial structure, but color-based biases may not generalize to colormaps with strong data spatial structure, like "hotspots" typically found in weather maps and neuroimaging brain maps. There may be a hotspot-is-more bias to infer that colors within hotspots represent larger quantities, which may override the dark-is-more bias. We tested this possibility in four experiments. Participants saw colormaps with hotspots and a legend that specified the color-quantity mapping. Their task was to indicate which side of the colormap depicted larger quantities (left/right). We varied whether the legend specified dark-more mapping or light-more mapping across trials and operationalized a dark-is-more bias as faster response time (RT) when the legend specified dark-more mapping. Experiment 1 demonstrated robust evidence for the dark-is-more bias, without evidence for a hotspot-is-more bias. Experiments 2 to 4 suggest that a hotspot-is-more bias becomes relevant when hotspots are a statistically reliable cue to "more" (i.e., the locus of larger quantities) and when hotspots are more perceptually pronounced. Yet, comparing conditions in which the hotspots were "more," RTs were always faster for dark hotspots than light hotspots. Thus, in the presence of strong spatial cues to the locus of larger quantities, color-based biases still influenced interpretations of colormap data visualizations.

Blue hues don't bring the blues: questioning conventional notions of color-emotion associations.

It is commonly held that yellow is happy and blue is sad, but the reason remains unclear. Part of the problem is that researchers tend to focus on understanding why yellow is happy and blue is sad, but this may be a misleading characterization of color-emotion associations. In this study, we disentangle the contribution of lightness, chroma, and hue in color-happy/sad associations by controlling for lightness and chroma either statistically or colorimetrically. We found that after controlling for lightness and chroma, colors with blue hue were no sadder than colors with yellow hue, and in some cases, colors with blue hue were actually happier. These results can help guide future efforts to understand the nature of color-emotion associations.

Estimating Color-Concept Associations from Image Statistics.

To interpret the meanings of colors in visualizations of categorical information, people must determine how distinct colors correspond to different concepts. This process is easier when assignments between colors and concepts in visualizations match people's expectations, making color palettes semantically interpretable. Efforts have been underway to optimize color palette design for semantic interpretablity, but this requires having good estimates of human color-concept associations. Obtaining these data from humans is costly, which motivates the need for automated methods. We developed and evaluated a new method for automatically estimating color-concept associations in a way that strongly correlates with human ratings. Building on prior studies using Google Images, our approach operates directly on Google Image search results without the need for humans in the loop. Specifically, we evaluated several methods for extracting raw pixel content of the images in order to best estimate color-concept associations obtained from human ratings. The most effective method extracted colors using a combination of cylindrical sectors and color categories in color space. We demonstrate that our approach can accurately estimate average human color-concept associations for different fruits using only a small set of images. The approach also generalizes moderately well to more complicated recycling-related concepts of objects that can appear in any color.

Mapping Color to Meaning in Colormap Data Visualizations.

To interpret data visualizations, people must determine how visual features map onto concepts. For example, to interpret colormaps, people must determine how dimensions of color (e.g., lightness, hue) map onto quantities of a given measure (e.g., brain activity, correlation magnitude). This process is easier when the encoded mappings in the visualization match people's predictions of how visual features will map onto concepts, their inferred mappings. To harness this principle in visualization design, it is necessary to understand what factors determine people's inferred mappings. In this study, we investigated how inferred color-quantity mappings for colormap data visualizations were influenced by the background color. Prior literature presents seemingly conflicting accounts of how the background color affects inferred color-quantity mappings. The present results help resolve those conflicts, demonstrating that sometimes the background has an effect and sometimes it does not, depending on whether the colormap appears to vary in opacity. When there is no apparent variation in opacity, participants infer that darker colors map to larger quantities (dark-is-more bias). As apparent variation in opacity increases, participants become biased toward inferring that more opaque colors map to larger quantities (opaque-is-more bias). These biases work together on light backgrounds and conflict on dark backgrounds. Under such conflicts, the opaque-is-more bias can negate, or even supersede the dark-is-more bias. The results suggest that if a design goal is to produce colormaps that match people's inferred mappings and are robust to changes in background color, it is beneficial to use colormaps that will not appear to vary in opacity on any background color, and to encode larger quantities in darker colors.

What color are emergency exit signs? Egress behavior differs from verbal report.

Illuminated emergency exit signs inform building occupants about safe egress routes in emergencies. These exit signs are often found in the presence of other colored signs, which may distract occupants when searching for safe exits. Such distractions can lead to confusing and even harmful outcomes, especially if occupants misinterpret the sign colors, mistaking non-exit signs for exit signs. We studied which colored signs people were most likely to infer were exit signs in a simulated emergency evacuation using virtual reality (VR). Participants were immersed in a virtual room with two doors (left and right), and an illuminated sign with different colored vertical bars above each door. They saw all pairwise combinations of six sign colors across trials. On each trial, a fire alarm sounded, and participants walked to the door that they thought was the exit. We tested two hypotheses: a local exposure hypothesis that color inferences are determined by exit sign colors in the local environment (i.e., red) and a semantic association hypothesis that color inferences are determined by color-concept associations (i.e. green associated with "go" and "safety"). The results challenged the local exposure hypothesis and supported the semantic association hypothesis. Participants predominantly walked toward green signs, even though the exit signs in the local environment-including the building where the experiment took place-were red. However, in a post-experiment survey, most participants reported that exit signs should be red. The results demonstrated a dissociation between the way observers thought they would behave in emergency situations (red = exit) and the way they did behave in simulated emergencies (green = exit). These findings have implications for the design of evacuation systems. Observers, and perhaps designers, do not always anticipate how occupants will behave in emergency situations, which emphasizes the importance of behavioral evaluations for egress safety.

Color, Music, and Emotion: Bach to the Blues.

When people make cross-modal matches from classical music to colors, they choose colors whose emotional associations fit the emotional associations of the music, supporting the emotional mediation hypothesis. We further explored this result with a large, diverse sample of 34 musical excerpts from different genres, including Blues, Salsa, Heavy metal, and many others, a broad sample of 10 emotion-related rating scales, and a large range of 15 rated music-perceptual features. We found systematic music-to-color associations between perceptual features of the music and perceptual dimensions of the colors chosen as going best/worst with the music (e.g., loud, punchy, distorted music was generally associated with darker, redder, more saturated colors). However, these associations were also consistent with emotional mediation (e.g., agitated-sounding music was associated with agitated-looking colors). Indeed, partialling out the variance due to emotional content eliminated all significant cross-modal correlations between lower level perceptual features. Parallel factor analysis (Parafac, a type of factor analysis that encompasses individual differences) revealed two latent affective factors- arousal and valence -which mediated lower level correspondences in music-to-color associations. Participants thus appear to match music to colors primarily in terms of common, mediating emotional associations.

Color inference in visual communication: the meaning of colors in recycling.

People interpret abstract meanings from colors, which makes color a useful perceptual feature for visual communication. This process is complicated, however, because there is seldom a one-to-one correspondence between colors and meanings. One color can be associated with many different concepts (one-to-many mapping) and many colors can be associated with the same concept (many-to-one mapping). We propose that to interpret color-coding systems, people perform assignment inference to determine how colors map onto concepts. We studied assignment inference in the domain of recycling. Participants saw images of colored but unlabeled bins and were asked to indicate which bins they would use to discard different kinds of recyclables and trash. In Experiment 1, we tested two hypotheses for how people perform assignment inference. The local assignment hypothesis predicts that people simply match objects with their most strongly associated color. The global assignment hypothesis predicts that people also account for the association strengths between all other objects and colors within the scope of the color-coding system. Participants discarded objects in bins that optimized the color-object associations of the entire set, which is consistent with the global assignment hypothesis. This sometimes resulted in discarding objects in bins whose colors were weakly associated with the object, even when there was a stronger associated option available. In Experiment 2, we tested different methods for encoding color-coding systems and found that people were better at assignment inference when color sets simultaneously maximized the association strength between assigned color-object parings while minimizing associations between unassigned pairings. Our study provides an approach for designing intuitive color-coding systems that facilitate communication through visual media such as graphs, maps, signs, and artifacts.

Modeling color preference using color space metrics.

Studying color preferences provides a means to discover how perceptual experiences map onto cognitive and affective judgments. A challenge is finding a parsimonious way to describe and predict patterns of color preferences, which are complex with rich individual differences. One approach has been to model color preferences using factors from metric color spaces to establish direct correspondences between dimensions of color and preference. Prior work established that substantial, but not all, variance in color preferences could be captured by weights on color space dimensions using multiple linear regression. The question we address here is whether model fits may be improved by using different color metric specifications. We therefore conducted a large-scale analysis of color space models, and focused in-depth analysis on models that differed in color space (cone-contrast vs. CIELAB), coordinate system within the color space (Cartesian vs. cylindrical), and factor degrees (1st degree only, or 1st and 2nd degree). We used k-fold cross validation to avoid over-fitting the data and to ensure fair comparisons across models. The best model was the 2nd-harmonic Lch model ("LabC Cyl2"). Specified in CIELAB space, it included 1st and 2nd harmonics of hue (capturing opponency in hue preferences and simultaneous liking/disliking of both hues on an opponent axis, respectively), lightness, and chroma. These modeling approaches can be used to characterize and compare patterns for group averages and individuals in future datasets on color preference, or other measures in which correspondences between color appearance and cognitive or affective judgments may exist.

Seasonal Changes in Color Preferences Are Linked to Variations in Environmental Colors: A Longitudinal Study of Fall.

People form associations between colors and entities, which influence their evaluations of the world. These evaluations are dynamic, as specific associations become more or less active in people's minds over time. We investigated how evaluations of colors (color preferences) changed over the course of fall, as color-associated fall entities became more prevalent in the environment. Participants judged their preferences for the same set of colors during nine testing sessions over 11 weeks during fall. We categorized the colors as Leaf and Non-Leaf Colors by matching them to leaves collected during the same period. Changes in preferences for Leaf Colors followed a quadratic pattern, peaking around when the leaves were most colorful and declining as winter approached. Preferences for Non-Leaf Colors did not significantly change. Individual differences in these changes could be explained by preferences for seasonal entities, as predicted by the differential activation hypothesis within the Ecological Valence Theory. The more a given individual liked fall-associated entities, the more their preference for Leaf Colors increased during fall. No analogous relations existed with winter-associated entities or Non-Leaf Colors. These results demonstrate the importance of studying temporal and individual differences for understanding preferences.

An ecological framework for temporal and individual differences in color preferences.

There are well-known and extensive differences in color preferences between individuals, but there are also within-individual differences from one time to another. Despite the seeming independence between these individual and temporal effects, we propose that they have the same underlying cause: people's ecological experiences with color-associated objects and events. Our approach is motivated by the Ecological Valence Theory (EVT; Palmer & Schloss, 2010) which states that preference for a given color is determined by the combined valence (liking/disliking) of all objects and events associated with that color. We define three ecologically-based hypotheses for explaining temporal and individual differences in color preferences concerning: (1) differences in object valences, (2) differences in color-object associations, and (3) differences in object activations in the mind when preferences are measured. We review prior studies that support these hypotheses and raise open research questions about untested predictions. We also extend the computational framework of the EVT by defining a single weighted average equation that captures both individual and temporal differences in color preferences. Finally, we consider other factors that potentially contribute to color preferences, including abstract symbolic associations, color in design, and psychophysical and/or physiological factors.

Colorgorical: Creating discriminable and preferable color palettes for information visualization.

We present an evaluation of Colorgorical, a web-based tool for creating discriminable and aesthetically preferable categorical color palettes. Colorgorical uses iterative semi-random sampling to pick colors from CIELAB space based on user-defined discriminability and preference importances. Colors are selected by assigning each a weighted sum score that applies the user-defined importances to Perceptual Distance, Name Difference, Name Uniqueness, and Pair Preference scoring functions, which compare a potential sample to already-picked palette colors. After, a color is added to the palette by randomly sampling from the highest scoring palettes. Users can also specify hue ranges or build off their own starting palettes. This procedure differs from previous approaches that do not allow customization (e.g., pre-made ColorBrewer palettes) or do not consider visualization design constraints (e.g., Adobe Color and ACE). In a Palette Score Evaluation, we verified that each scoring function measured different color information. Experiment 1 demonstrated that slider manipulation generates palettes that are consistent with the expected balance of discriminability and aesthetic preference for 3-, 5-, and 8-color palettes, and also shows that the number of colors may change the effectiveness of pair-based discriminability and preference scores. For instance, if the Pair Preference slider were upweighted, users would judge the palettes as more preferable on average. Experiment 2 compared Colorgorical palettes to benchmark palettes (ColorBrewer, Microsoft, Tableau, Random). Colorgorical palettes are as discriminable and are at least as preferable or more preferable than the alternative palette sets. In sum, Colorgorical allows users to make customized color palettes that are, on average, as effective as current industry standards by balancing the importance of discriminability and aesthetic preference.

Seasonal Variations in Color Preference.

We investigated how color preferences vary according to season and whether those changes could be explained by the ecological valence theory (EVT). To do so, we assessed the same participants' preferences for the same colors during fall, winter, spring, and summer in the northeastern United States, where there are large seasonal changes in environmental colors. Seasonal differences were most pronounced between fall and the other three seasons. Participants liked fall-associated dark-warm colors-for example, dark-red, dark-orange (brown), dark-yellow (olive), and dark-chartreuse-more during fall than other seasons. The EVT could explain these changes with a modified version of Palmer and Schloss' (2010) weighted affective valence estimate (WAVE) procedure that added an activation term to the WAVE equation. The results indicate that color preferences change according to season, as color-associated objects become more/less activated in the observer. These seasonal changes in color preferences could not be characterized by overall shifts in weights along cone-contrast axes.

Music-to-Color Associations of Single-Line Piano Melodies in Non-synesthetes.

Prior research has shown that non-synesthetes' color associations to classical orchestral music are strongly mediated by emotion. The present study examines similar cross-modal music-to-color associations for much better controlled musical stimuli: 64 single-line piano melodies that were generated from four basic melodies by Mozart, whose global musical parameters were manipulated in tempo(slow/fast), note-density (sparse/dense), mode (major/minor) and pitch-height (low/high). Participants first chose the three colors (from 37) that they judged to be most consistent with (and, later, the three that were most inconsistent with) the music they were hearing. They later rated each melody and each color for the strength of its association along four emotional dimensions: happy/sad, agitated/calm, angry/not-angry and strong/weak. The cross-modal choices showed that faster music in the major mode was associated with lighter, more saturated, yellower (warmer) colors than slower music in the minor mode. These results replicate and extend those of Palmer et al. (2013, Proc. Natl Acad. Sci. 110, 8836-8841) with more precisely controlled musical stimuli. Further results replicated strong evidence for emotional mediation of these cross-modal associations, in that the emotional ratings of the melodies were very highly correlated with the emotional associations of the colors chosen as going best/worst with the melodies (r = 0.92, 0.85, 0.82 and 0.70 for happy/sad, strong/weak,angry/not-angry and agitated/calm, respectively). The results are discussed in terms of common emotional associations forming a cross-modal bridge between highly disparate sensory inputs.

Ecological Effects in Cross-Cultural Differences Between U.S. and Japanese Color Preferences.

We investigated cultural differences between U.S. and Japanese color preferences and the ecological factors that might influence them. Japanese and U.S. color preferences have both similarities (e.g., peaks around blue, troughs around dark-yellow, and preferences for saturated colors) and differences (Japanese participants like darker colors less than U.S. participants do). Complex gender differences were also evident that did not conform to previously reported effects. Palmer and Schloss's (2010) weighted affective valence estimate (WAVE) procedure was used to test the Ecological Valence Theory's (EVT's) prediction that within-culture WAVE-preference correlations should be higher than between-culture WAVE-preference correlations. The results supported several, but not all, predictions. In the second experiment, we tested color preferences of Japanese-U.S. multicultural participants who could read and speak both Japanese and English. Multicultural color preferences were intermediate between U.S. and Japanese preferences, consistent with the hypothesis that culturally specific personal experiences during one's lifetime influence color preferences.