1. INTRODUCTION

Colors tend to influence the overall impression of objects and visual environments. Influences arising from a chromatic change in illumination, commonly on a locus of color temperature, are one of the main current topics in color constancy work [1]. In research on the application of color science and technology, the most popular current topic is the analysis of distribution and usage of colors in architecture, room interiors, and objects geared towards answering the question of how colors should be used in those scenarios to achieve more attractive and comfortable color design. This popularity suggests that although there are differences in degree among the claims of color researchers, the psychological effects of color are widely recognized in general.

In color design, the simplest method is to compare alternative colors for objects in environments, as presented on a monitor or on printed paper by designers and possible users of those objects. If there are many choices of colors for selection, however, this kind of comparison is time-consuming and tends to be difficult, especially for naïve observers. Thus, in order to reduce the number of comparison choices, it is common to use color impression maps [2] obtained in advance by measurement of color impressions by means of a semantic differential (SD) method. In the SD method, each color is evaluated in the context of many pairs of semantic words with a grade point (e.g., $-3$, $-2$, $-1$, 0, 1, 2, 3) set for each pair of semantic words [3,4]. For example, if a pair of semantic words is “warm–cool”, the impressions of perfect “warm” and perfect “cool” are graded by the minimum value (e.g., $-3$) and the maximum value (e.g., 3), respectively; the impression between these extremes is graded by a value between $-2$ and 2. In the traditional approach, all sets of the grade points for all paired semantic words are subjected to a factor analysis to find the few factors that can explain the tendency of the color impression. A principal component analysis (PCA) is also commonly used to analyze the data in which the sum of distances between items becomes maximum in distribution [5]. Traditional research [2,6] suggests two main factors, “heat” (warm–cool) and “softness” (soft–hard) to set a reasonable distribution of impressions of single colors. More recent studies involving the impressions of two-color combinations suggest three main factors, “activity” (active–passive), “weight” (heavy–light) and “heat” [7], although “activity” is one of three core factors [activity, potency (superior–inferior or powerful–powerless) and evaluation (beautiful–ugly or favorable–unfavorable)] in evaluation by the SD method [3,4] so it is natural that “activity” would be used in explanations of color distribution. It has been reported that the factors “brightness” (lightness; light–dark) and “softness” are close in the distribution map [8].

We would like to mention, however, that a few factors found by the factor analysis and PCA are strongly dominant in the case of color evaluation. Thus, it cannot be determined whether other possible factors, which are mostly the integrated meanings of some semantic terms in the SD method, are reasonable expressions of color impressions; this is because it is impossible to distinguish cases in which smaller loadings of these semantic words to the factor (or the principal component) were simply showing the less-dominant-but-important impression from cases where those semantic words were not suitable for color impression and hence grading had little meaning. Thus, a method for evaluating colors precisely by means of words must be considered.

Psychological effects of colors are not necessarily limited to colored objects: colors are also expected to have an effect on the drawing of meaning from words. The most famous example of this is Stroop color interference [9,10]. Considering a less extreme case, we thought the possibility that impressions of semantic words could be evaluated in terms of colors as being in the opposite direction of the usual evaluation tasks, in which impressions of colors are evaluated using semantic words in the SD method. Regarding the case of semantic words expressing a simple concept like “hot,” the relationship between the word and color, which can be referred to as color-word association, is simple and tight. A color impression (i.e., red) can be strongly combined with a word impression (i.e., hot) as a result of the impressions in daily life. For example, in the case of the simple word, “cold,” the related color impression is thought to be easily obtained by retroactive reflection on the impression of the word under the color-word association; blue or bluish color will be selected to match. Thus, it is expected that in many simple-meaning semantic words, the impression of a word can be obtained via the memorized color impression under the color-word association obtained by experiences.

It is not yet clear, however, whether the impression of semantic words representing complex concepts (such as “tranquil”) can be expressed by selection of colors, since we usually do not have experiences connecting such words to colors. Therefore, in this study, we examined whether the impression of a semantic word can be represented stably by hue. From the outset, we expected that it would be difficult to create an experiment using an adjusting method (i.e., changing the color freely to match a semantic word) or a scaling method (i.e., rating the degree of matching by numeric values), since a range of colors (hues) obtained in the matching and a deviation of the scaling values might be extremely large and subjects would not be confident to their decisions. Thus, we employed a paired comparison method (also known as pairwise comparison method) in which the judgement results would be expressed by selection rates from 0 to 1 for the evaluation process. We investigated the relationship between word impression and color impression by having the subjects select a hue for a word meaning via the color-paired comparison method. Two colors from among 132 combinations of 12 hues were simultaneously presented, and the subject selected the one hue closer to the impression of an evaluative word. In this study, we varied only hues. The influences of saturation (chroma) and lightness were excluded because the number of choices (colors in this study) had to be kept small in the paired comparison method.

In addition, we also observed the evaluation of hues by semantic words as the traditional SD method. Both of the data sets were analyzed by PCA as explained in the Results section. In the experiment using the new method based on the PCA, each semantic word had the optimized contribution values of principal components (PCs) in the best fit to the hue evaluation data by a linear combination of PCs; semantic words were distributed in the space of the PC axes reflecting the contribution values. Conversely, in the PCA of the data from the SD method, the contributions of semantic words were expressed by loading values to each PC, and the words were distributed in the space of the loading value axes of PCs. In the space of the loading value axes of the PCs obtained from the data of the SD methods, similar words would be distributed in closer positions. Depending on previous literature [2,6], the axes might be expressed by “heat” (warm–cool) and “softness” (soft–hard). From expectation to symmetry to that result in opposite directions, we initially hypothesized that the distribution of hues in the space of the loading value axes of PCs obtained from the new methods would be dominated by the similarity of hues in terms of axes [e.g., warm colors and soft (pastel) colors] with grouping by color categories [11–13]. The results of this study, however, indicate that the initial hypothesis was not true. The distribution of hues was expressed by a hue circle.

If there is a bidirectional relationship between semantic words and hues, and if it is stable, the two distributions of the word impressions should be similar after linear expansion and rotation. If there is no bidirectional relationship to which the coordinates of words do correspond, it would be too artificial to connect such semantic words (not words like “hot” and “cold”) to hues. Thus, we expected the comparison of the coordinates of the words to show the appropriateness of connections between words and hues. This means that this comparison enables us to classify the association between hue and concept. By this methodology, in the future it will be possible to investigate the process of color-concept association in the human brain using differences of brain activities measured by fMRI between these tasks and between strong and weak associations.

2. METHODS

A. Subjects

Ten color-normal subjects (six female and four male) of age 19 to 25 (mean, 22.0) participated in the experiment involving evaluation of word impression by hue and in a controlled experiment. Eleven color-normal subjects (six female and five male) of age 19 to 25 (mean, 22.0) participated in the experiment involving evaluation of color impression via the SD method. Five subjects (one female; four male) participated in both experiments. All subjects were Japanese and naïve regarding colorimetry, color psychology, and the purpose of each experiment; the authors did not serve as subjects. All subjects had normal or corrected-to-normal acuity with best-corrected visual acuity (BCVA) better than 0.6 (spatial resolution equal to or smaller than 1.67 min of visual angle). The color vision of subjects was tested by a set of color vision tests: Ishihara color test plates (International 38 plates edition), the Farnsworth D-15 test, and standard pseudo-isochromatic plates (SPP).

The procedures and experiments in this study conform to the principles expressed in the Declaration of Helsinki and were approved by the Kochi University of Technology Research Ethics Committee. Written informed consent was obtained from each subject prior to testing.

B. Apparatus and Calibration

Color stimuli were presented on a 16-inch (40.6 cm) cathode ray tube (CRT) monitor (CPD-G220, Sony) placed in a dark room with no ceiling lighting during measurements. The distance between the monitor screen and subject eyes was 55 cm. Colors of the stimuli were controlled by a Windows OS application that provides 8-bit resolution for each RGB phosphor in a Dell PC, and gamma correction of the monitor was not carried out. The accuracy of color stimuli, however, was provided by calibration because we did not use the color adjustment method and all color stimuli were fixed for each set of luminance and chromaticity coordinates. No mouse or keyboard was used for subject responses; all responses were handwritten by the subject and the experimenter.

Chromaticity coordinates and luminance of all colors in the stimuli, measured by colorimeter (CS-200, Konica-Minolta, Inc.) and spectral radiometer (CS-1000, Konica-Minolta, Inc.), confirmed that screen presentation error was less than 3% for Commission Internationale de l'Éclairage (CIE) 1931 $xy$ chromaticity coordinates and less than 5% for luminance throughout the duration of the experiments.

C. Color Stimulus

Twelve stimulus colors were selected from vivid tones in the practical color coordinate system (PCCS) by Japan (Nihon) Color Research Institute. In the PCCS, tone is defined as that set of hues that yield the same color image. The vivid tone is the set of mostly saturated colors corresponding to lightness from /10 to /14 in Munsell value. It should be noted that in the PCCS, the luminance of the same tone chips was systematically changed to create the same tone, instead of keeping equal lightness or equal luminance. We selected 12 color chips from 24 vivid tone color chips, and colors were presented on the monitor under D65 illumination simulation set to luminance of $77.2\mathrm{cd}/{\mathrm{m}}^2$ on a standard white plate. Luminance of the gray background was $12.6\mathrm{cd}/{\mathrm{m}}^2$, which is equivalent to N4.57 in the Munsell system, meaning no blackness induction on the colors of the rectangles [14,15]. Figure 1 (top panel) shows luminance of colors and background gray. Figure 1 (bottom panel) shows chromaticity coordinates of stimulus colors, background gray, and D65 in CIE 1974 u’v’ chromaticity diagram. In the experiment involving evaluation of color impression by the SD method, three colors were added: white, gray, and black, which were the same as the D65 white, the background gray, and the black of the border line, respectively.

 

Fig. 1. Luminance (top panel) and chromaticity coordinates (bottom panel) of 12 stimulus colors. (Top panel) Circles and squares denote luminance of color chips and background gray (BkG) (N4.57), respectively. (Bottom panel) Color chip number and PCCS names are presented near each point. Circle and cross denote chromaticity coordinates of BkG and D65 (on standard white plate), respectively.

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One color rectangle was $7.0\mathrm{deg}(\text{width})\times 6.4\mathrm{deg}(\text{height})$ in visual angle, edged with black lines of 10 min in width. In the paired comparison experiment, two rectangles were presented side by side with 2 deg gap (cf. Fig. 3); otherwise only one chromatic rectangle was presented in the center of the screen. In all presentations, the chromatic rectangle was shifted 1.86 deg below vertical center for subject comfort during continuous viewing.

D. Semantic Words for Evaluation

We used Japanese words because all subjects in the study were Japanese students. However, in this paper we mostly refer to these words by their English translations. In order to decide the semantic words for evaluation by hue in this study, we first analyzed the data from a previous study [16] involving evaluation of colors by the SD method. That study used ten of the eleven basic colors (red, orange, yellow, brown, green, blue, purple, white, gray, and black, with pink excluded); three mixed colors (bluish-purple, yellowish-green, and reddish-blue); and seven commonly used colors [skin tone, cream, water, ocher (sand or mud), grassy, wine-red, and iron]. These selected colors correspond well to the recent study of Japanese color usage [13]. Their observers were asked to evaluate these colors, drawing from twenty-five Japanese paired-semantic words. The positive items in the word pairs were soft, beautiful, delicate, deep, fresh, sweet, strong, warm, bright, grand, full, exciting, hard, smooth, thick, salty, vivid, erotic, cloudy, clear, sharp, permanent, comfortable, watery, and light. We performed PCA analysis on the mean data of 72 subjects (32 male and 42 female) and analyzed 25 semantic words by obtained loading values of the first, second, and third PCs. Figure 2 shows the distribution of 25 semantic words as coordinates of the first and second PC loading value axes. In Fig. 2, the abscissa was reversed to place negative values on the right side for better comparison in later discussion. Because many of the 25 words were distributed in the positive direction of the second PC loading value, we set five antonyms denoted by dark-yellow lines and words in bold black font, as seen in Fig. 2.

 

Fig. 2. Distribution of 25 semantic words (denoted by smaller font size) and categories, for determining new semantic words (denoted by ellipses and words in sky-blue fonts) defined by the first and second PC loading values calculated from the data of a previous study [16]. Semantic words are shown near their symbols. Red, blue, and purple fonts denote that the absolute loading values of those semantic words are greater than 70% of the absolute maximum loading value in the first, second, and third PCs, respectively. Dark-yellow lines and words in bold black font denote antonyms set in this study. See the text for details.

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We divided the semantic words into seven categories based on the distribution of the first and second PC loading values and one additional category based on the third PC loading value. Although unlike the case of factor analysis, here factors for determining the distribution were not necessarily clear from the PCA, so we inferred that the PCA shows the mathematically most-separated data distribution and can still be useful for categorization of the words. We set eight new semantic words corresponding to these eight categories, giving consideration to the semantic words in each category. Those eight words were GENKI-NA (vigorous), NODOKA-NA (tranquil), JYUUKOU-NA (massive), KAGEKI-NA (extreme), SEIREN-NA (clean), SABIRETA (deserted), SENSAI-NA (fine), and SOUREI-NA (magnificent). We added one more word, MEDATSU (visible), because visibility of color is one of the important topics in current color research, especially work towards application.

In the experiment involving evaluation of color impression by the SD method, we used 35 semantic words: nine semantic words for the main experiment, the 25 words used in a previous study [16], and one additional word, KIHAKUNA (thin) as an antonym to KOI (thick) to fill an empty space (bottom-center area) as shown in Fig. 2.

E. Procedure

In the experiment involving evaluation of word impression by hue, a gray background was first presented to each subject for 5 min; Figure 3 shows the stimulus presentation. After the background adaptation period, one word for evaluation was presented until the subject agreed to start the trials. After that, two color rectangles were presented simultaneously side by side in pseudo-random order for all 132 combinations successively. The subject was asked to select the one color of each pair of colors that was closer to the word impression, reporting by oral response (left or right). A set of 132 trials took 8–10 min, and all nine words were measured in random order in one session. Three sessions were conducted for each word for each subject, meaning that one color combination under one word was tested in six trials (each color placed three times on the right and three times on the left).

 

Fig. 3. Stimulus presentation for evaluation of word impression by hue. The words were written in Japanese (“tranquil” in this diagram).

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In the experiment involving evaluation of color impression via the SD method, after the 5 min background adaptation period, one color rectangle was presented, and the subject evaluated the color by writing a “√” mark on a line scale of seven plus-shaped cross sections (denoting $-3$. $-2$. $-1$, 0, 1, 2, 3, although the numbers were not shown) for each paired semantic word. It also took 6–9 min to assess all 35 word pairs for one color. Each color was presented until the subject completed the evaluation. All twelve colors and three additional colors (white, black, and gray) were evaluated in one session in pseudo-random order, and three sessions were performed on different days for one subject.

F. Control Experiment

In order to verify the experimental goal of evaluating word impression by hue, it is important to confirm independence between colors and between evaluative words. If the colors and evaluative words were not independent of each other, the evaluation results would usually be arbitrary since one color and one word could be easily replaced by another color and another word, respectively.

We asked the subjects to perform color naming for each hue (color chips) using one of twelve color names: eleven basic color terms (red, green, blue, yellow, pink, orange, purple, brown, white, gray, and black); and one color name (yellowish-green) used frequently in Japanese culture [11]. We did not use some color terms frequently used by the Japanese [e.g., MIZU (water) and HADA (skin tone)] [11,13], since we expected to perform this method in other languages in the future and we were afraid that such specific terms would not be able to be translated to other languages accurately, as well described by Kuriki et al. (2017) [13]. Figure 4 shows the result of the color naming. Responses of yellowish-green were treated as half yellow and half green responses in calculation. The twelve stimulus colors were separated into seven categories: red (v2), orange (v4 and v6), yellow (v8), green (v12), blue (v14, v16, and v18), purple (v22), and pink (v24). The most selected color name was selected in less than 80% of cases in v10 (separated to yellow and green) and v20 (separated to blue and purple). The results indicate that the 12 stimulus colors would be sufficient to describe a maximum of seven independent impressions. We would like to mention that colors were not perfectly separated; color categories of orange and blue have two and three colors, respectively. This means that if the distribution of hue would be expressed by color categories in the evaluation of semantic words, these two and three colors would be treated as almost the same color in the distribution; this point will be addressed in the Discussion section.

 

Fig. 4. Mean of color naming ratio for each color chip. Color names of red (denoted by small squares), orange (light triangle), yellow (light circles), green (large squares), blue (dark circles), purple (dark triangles), and pink (diamond) appeared in color naming task. Responses of yellowish-green were treated as half yellow and half green responses in calculation.

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Nine evaluative semantic words were evaluated by the SD method. The impressions of the words were graded from $-3$ to 3 for three core words [activity (active–inactive), potency (superior–inferior), and evaluation (beautiful–ugly)] [3,4]. Figure 5 shows the mean grading for nine words. As can be seen in the right panel of Fig. 5, for nine words, evaluation and potency are not independent; they are strongly correlated with a coefficient of determination of 0.80. This means that the grading of potency can be predicted by the grading of evaluation and vice versa, although this correlation was dominated by the point of “deserted,” and without that point the coefficient of determination would be 0.13. Conversely, activity and evaluation are independent of each other regardless of the point of “deserted.” Blue ellipses in Fig. 5 show the categories of the words with absolute values greater than 80% of the maximum absolute values on each axis. Black ellipses show the categories of words with absolute values less than 80%. These results suggest that nine evaluative words are well enough separated conceptually in at least five categories that are independent of each other. The distribution of the words, however, can be explained by the two independent axes; this suggests that it is not surprising that these semantic words would be expressed by hues that have two dimensions (as described by red-green and yellow-blue chromatic-opponent channels).

 

Fig. 5. Distribution of nine semantic word impressions plotted as activity versus evaluation coordinates (left panel) and as evaluation versus potency coordinates (right panel). Semantic words are shown near the symbols. Blue and black ellipses denote categories defined by grading scores (see the text for details). $R^2$ denotes the coefficient of determination.

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3. RESULTS

A. Selection Rate of Hue for Semantic Word

We used the color-paired comparison method for the experiment involving evaluation of word impression in terms of hue. The results are initially shown as the number of wins in the paired comparison for each hue. Although the number of wins and the selection rate are not nonlinear, we first modified number of wins before calculating the selection rate: 6 wins (all wins) was modified to 5.5 wins and 0 wins (no wins) was modified to 0.5 wins. In addition, we set the modified selection rate by subtracting 0.5 from the selection rate, calculated as the number of wins divided by 6. Thus, the modified selection rate for all wins, 3 wins–3 losses, and no wins data becomes 0.417, 0, and $-0.417$, respectively. That modification helped to avoid unexpected distortions in calculated-PCA results and model curve fits to the selection rate data because the number of comparisons was just six (trials) for each semantic word and for each subject, and the total of all wins and no wins data could be obtained with ten subjects.

Figure 6 shows the selection rate data as a function of hue (denoted by color chip number) for all semantic words. The order of the panels (left top to left bottom and right top to right bottom) is the order of the activity points (descending order) in Fig. 5. Error bars denote $\pm 2\mathrm{S.E.M}$. (doubled standard error of the mean), which show a 95% confidence interval ($\text{accurately}\pm 2.23\times \mathrm{S.E.M}$. for $N=10$). The blue curves are model fits using the first and second PCs (explained in the next subsection). Considering the error bars, the data for “visible” and “vigorous” are almost identical; the data for “visible” and “vigorous” show a maximum selection rate at yellowish-orange (v6) to yellow (v8) and a minimum selection rate at violet (v20) to purple (v22). The data for “extreme” have a similar tendency, with a maximum at red (v2) to reddish-orange (v4) and a minimum at blue-green (v14) to violet (v20). For other semantic words, however, the hues of the maximum and minimum selection rates shift in the greenish and reddish directions, respectively. The data for “tranquil” have hues closest to the maximum and minimum selection rates compared to the data for “visible,” “vigorous” and “extreme”; the selection rates have a maximum around yellowish-green (v10) to green (v12) and a minimum around purple (v22) to red (v2). In the data for “fine,” “clean,” “magnificent,” and “deserted,” the hues of the maximum selection rate shifted to blue-green (v14), greenish-blue (v16), blue (v18), and violet (v20), respectively. In the data for these four words, the hues of the minimum selection rate were reddish-orange (v4), red (v2), red-purple (v24), and red (v2), respectively. The data for “massive” are most different from those for “visible” and “vigorous”; the hues of the maximum and minimum selection rates are purple (v22) and yellow (v8), respectively. These hues are complementary colors of the hues of the maximum and minimum in the data for “visible” and “vigorous.”

 

Fig. 6. Modified selection rate as a function of hue (denoted by color chip number) for nine semantic words. The order of the panels (left top to left bottom and right top to right bottom) is the descending order of activity points in Fig. 5. Error bars denote $\pm 2\mathrm{S.E.M}$. Blue curves and dots are fits by PCA-based model (see the text for details).

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It is interesting that the selection rates changed gradually in continuous hue for all semantic words, although the hues could be separated into seven distinct categories, as shown in Fig. 4. This indicates that assignment of hue to semantic words does not depend on the individual impression of a single hue, but rather on the set of neighboring hues in the hue circle. In addition, the hues with the maximum and minimum selection rates for one semantic word are almost complementary. Unexpectedly, human subjects evaluated semantic word impressions on a scale of complementary-paired colors (hues) corresponding to the maximum and minimum selection rates with tracing hues in hue-circle order for moderate selection rates. This phenomenon will be described in more detail in the next subsection.

B. Principal Component Analysis to Selection Rate Data

1. Color Distribution Expressed by First and Second Principal Component Loadings

We knew of the possible factors of hues as described in the Introduction section, however, it was too difficult to estimate those factors in order to determine the distribution of semantic words used in this study. Although a factor analysis provides more factors to explain an entire data set, for the purpose of this study it is not necessarily needed to analyze the data by many factors as in the studies of semantics. Thus, we decided to use the PCA, in which the number of PCs (dimensions) reaches minimum. The sum of distances between items (the deviation of the data) reaches maximum in the distribution defined by the first PC, and the second and above PCs are determined in the same way under the restraint condition of orthogonality [5]. The PCA was applied to the data of subject-averaged modified selection rates of each hue for the nine evaluative words; the proportion of variance from the first to fourth PCs was 67.76%, 26.80%, 3.71%, and 1.30%, respectively. The cumulative contribution rates from the first to fourth PCs were 67.76%, 94.56%, 98.27%, and 99.58%, respectively. For that reason, we thought to use only the first and second PCs in further analysis.

Loading values for the first and second PCs for each of the stimulus hues show the contribution of color to the evaluation of all words through the PCs. Figure 7 shows the loading values of the first and second PCs for each color and the distribution of hues defined by the loading values for the first and second PCs. The black ellipse shows the best fit to all data points: the lengths of the longer and shorter axes are 0.521 and 0.347, respectively, and the axis ratio is 1.50. It is surprising that the contribution of hues to the modified selection rates of semantic words is described by the hue circle (ellipse) maintaining antagonistic coordinates of colors placed at the opposite positions in the original PCCS hue circle (e.g., v2 versus v14; v8 versus v20). Further argument in this vein will be presented in the Discussion section.

 

Fig. 7. Loading values of first and second PCs (top panel) and distribution of hues as defined by the first and second PC loading values (bottom panel). (Top panel) Circles and squares denote first and second PCs, respectively. (Bottom panel) Color chip number and names in PCCS are presented near each point. The black ellipse denotes the best fit to all data points.

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2. Model Prediction by First and Second Principal Components

In light of the concept underlying the PCA, it was expected that the selection rates could be fitted by a simple linear summation model of the two PCs with two weight coefficients for each PC. Because we used the modified selection rates, we did not need to introduce an offset coefficient. These two weight coefficients were separately optimized for different semantic words so as to reduce the error between the data points and the model prediction. The blue curves in Fig. 6 are the best fits by the model. As expected from the high cumulative contribution rate of 94.56% for the first and second PCs, the linear model fits the data well, and more than 75% of values predicted by the model were within the approximated 95% confidence interval, as shown by the error bars of $\pm 2\mathrm{S.E.M}$.

We compared the modified selection rates with the model prediction values. For all nine evaluative words, the rates and values were significantly and positively correlated ($p<0.05$); the mean of the coefficient of determination ($R^2$) was $0.90\pm 0.08$. The minimum coefficient of determination ($R^2$) was 0.71, for “magnificent” and the next smallest was 0.85 for “deserted.” These results suggest that the model prediction is accurate and the modified selection rates can be expressed by two factors (a two-dimensional expression). Additionally, it was found that the twelve color stimuli used in the experiment were handled according to the ability of hues to express the concepts of the semantic words.

3. Word Distribution Expressed by Optimized Weight Coefficients of First and Second Principal Components of the Model

In the PCA, score sets were calculated as the weight parameters of each PC’s contribution to a semantic word. The scores of the first and second PCs for each word indicate how the word is expressed by sets of hues and show the distributions of all words. The distributions of words expressed by these scores, however, would be identical (except for a multiple coefficient) with the distribution by optimized weight coefficients of the model using the first and second PCs obtained in the previous subsection, since the cumulative contribution rate of the first and second PCs was quite high (94.56%).

Figure 8 shows the distribution of semantic words obtained as the optimized weight coefficients for the first and second PCs. We categorized semantic words according to the absolute values of the weight coefficients. The blue ellipses in Fig. 8 denote categories defined by absolute values greater than 70% of the maximum absolute values. There are three such categories; the first category has a large negative contribution from the first PC and includes “visible,” “vigorous,” and “extreme.” The function shapes of the modified selection rates were similar, as can be seen in Fig. 6, and the hue of the maximum selection rate was in the neighborhood of red to yellow. The second and third categories have higher and lower values for the second PC; the second category includes “tranquil,” and the hue of the maximum selection rate was in the neighborhood of yellowish-green to green. The third category includes “massive,” whose data are most different from those of “visible” and “vigorous.” The fourth category includes the rest of the words: “clean,” “fine,” “magnificent,” and “deserted.” Although it is not clear that all of these words should be placed in one category, the hues of those with maximum selection rates were relatively close.

 

Fig. 8. Distribution of semantic words obtained by optimized weight coefficients for first and second PCs. Squares denote the coordinates of semantic words shown near the symbol. Square colors denote the hue of the maximum selection rate. Blue ellipses denote categories defined by absolute values greater than 70% of the maximum absolute values (see the text for details).

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C. Evaluation of Color Impression by Means of the SD Method

We also conducted an experiment involving the evaluation of color impression by means of the SD method using 35 semantic words. The PCA was applied to the data (subject-averaged grading points for each semantic word for the twelve colors [nine hues, white, gray, and black]); the proportions of variance from the first to fourth PCs were 45.25%, 27.22%, 14.16%, and 5.55%, respectively. The cumulative contribution rates from the first to fourth PCs were 45.25%, 72.47%, 86.64%, and 92.18%, respectively. This means that it is more appropriate to use the first three PCs to express the results of the PCA. For the comparison of the results with those of evaluations of word impression by hue, however, we used only the first and second PCs for further analysis.

In the results of the evaluation of color impression, loading values of the first and second PCs for each semantic word show the contribution of words to the evaluation of all colors through the PCs. Figure 9 shows the distribution of semantic words defined by the first and second PC loading values. The results, shown in Fig. 9, should theoretically be the same as those in Fig. 2, although the colors for evaluation were different. These two results appear to have totally different structures, but if the grades of the seven core semantic words (except “extreme” and “tranquil”) in Fig. 9 were flipped along the axis connecting the points for “extreme” and “tranquil” (denoted by the dotted line in Fig. 9), the structure of the data points would become similar except the data of “magnificent,” which had a high loading value of the third PC in both results and was not determined by the first and second PC loading values. The comparison between the results in Figs. 8 and 9 will be described in the Discussion section.

 

Fig. 9. Distribution of 9 core semantic words (denoted by sky-blue font) and 26 semantic words (denoted by smaller size black font) defined by the first and second PC loading values. Semantic words are shown near their symbols. The symbol colors for 9 core semantic words were obtained from Fig. 8. The dotted line denotes the connection between “extreme” and “tranquil.” See the text for details.

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The scores of the first and second PCs for twelve colors give an indication of how color is expressed by sets of semantic words. Figure 10 shows the distribution of all colors obtained from the first and second PC score values. In this result, the black ellipse, showing the best fit to nine hue points (white, gray, and black were excluded), is slanted 49.42 deg from the vertical line, and its center is shifted to ($-0.736$, $-0.274$). As shown in Fig. 10, the distribution of hues basically maintains the structure of the hue circle, but some points are strongly distorted, especially those for yellow-green (v10), blue-green (v14), and greenish-blue (v16). This point and its comparison with the result shown in Fig. 7 will be discussed in the Discussion section.

 

Fig. 10. Distribution of 9 hues, white, gray and black, obtained from the first and second PC score values. Color chip number and names in PCCS are presented near each point. The black ellipse denotes the best fit to all hue points (white, gray, and black excluded).

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4. DISCUSSION

A. Semantic Word Impression by Hue

As described in the Results section, the selection rates for evaluation of semantic words changed gradually under continuous hue; there was no drastic change in the selection rate under continuous hue change such as was found in the color naming experiment. This indicates that assignment of hue to semantic words does not depend on the categorical color; word impression was expressed by a set of hues in the order of the hue circle. That is also confirmed by the fact that the hues of the maximum and minimum selection rates for one semantic word are almost complementary colors and antagonistic combinations in the hue circle, as shown in Fig. 7. We would like to mention again that hues showing about zero modified selection rates for one word are also not random, nor do they show a steep change. In addition, the hues never gathered at a specific location, and this is considered as an indication that categorical processing of color [11–13,17] has not been performed. Instead, it unexpectedly suggests that gradual changes of chromatic opponent responses must be used in higher processes for this task; it does not resemble the yes–no type of change (one-bit change) seen in classification of color categories.

It is surprising that the contribution of hues to the modified selection rates of semantic words is described by the hue circle, maintaining antagonistic coordinates of colors placed at the opposite positions in the original PCCS hue circle. It also means that semantic word impressions can be described by hues that have only two dimensions. In addition, similar to the concept of hue circles, two dimensions for word impressions can be explained by red–green and blue–yellow chromatic opponent channels in color theory [18]. This may reflect the fact that complex impressions of semantic words commonly have a relationship with color impressions that depends little on cognition and memories constructed by language and experience; it may mean that outputs of signal of color information processes are used for higher-order cognition of word meanings. The other possibility is that the neural outputs of color processing are used to associate word meanings to sensory base processing.

However, we have to give serious consideration to the fact that the color selection results for semantic words were reproducible using two variables. First, this is easily explained by the fact that the colors used in this study were in the same hue circle with the same tone, and that all differences among these hues could be expressed by two-dimensional variables. This points to the interesting possibility of a phenomenon where the semantic words could also be evaluated using two-dimensional variables. We regret to say, however, that this point involves too much approximation in the PCA treatment. In the case of the use of hues, the cumulative contribution rate from the first to the second PC was 94.56%, but that same rate was only 72.47% in the SD measurement. Thus, it is likely that three or four dimensions of the semantic words were approximated by two dimensions because the hue had only two dimensions. From this argument, the idea emerges of using a three-dimensional color set to evaluate semantic words, with variations of hue, saturation, and lightness. If this argument were sufficiently accurate, the semantic words could be evaluated more precisely with colors. This point should be tested in the future.

The results of selection rates, shown in Fig. 6, and the distribution of semantic words, shown in Fig. 8, suggest the presence of two series of words; one is “visible,” “vigorous,” and “extreme.” The other is “tranquil,” “clean,” “magnificent,” “fine,” “deserted,” and “massive.” As described in the next subsection, however, this categorization must depend on suitability of words for evaluation with hues. Considering that point, we would like limit our claim to two categories, not series of words, because of scattering in the order of words in this study (see the next subsection); one category is “visible,” “vigorous,” and “extreme,” and the other is “clean” and “massive.”

 

Fig. 11. Distribution of semantic words obtained by optimized weight coefficients of hue selection (denoted by squares) and by loading values of the SD method (circles) in a modified scale for first and second PCs. For hue selection, the coordinates were compressed and rotated as shown by the scale vectors (red arrows) for the first and second PCs, indicating abscissa (first PC) and ordinate (second PC) vectors of length 0.5 in the original coordinates (Fig. 8). Semantic words are shown near the related symbols. Colors of squares denote the hue of the maximum selection rate. Longer distances between two data points are connected by dotted lines for ease of visibility (see the text for details).

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Although we excluded white, gray, and black in the color-paired comparison method experiment so as to reduce experimentation time, the score results for the SD method, shown in Fig. 10, indicate that white, gray, and black do not exist on the ellipse reflecting the hue circle. Because the points are plotted in the coordinates of the PCs, it is not surprising that neutral colors are not placed at the center of the ellipse. Rather, the placement of white, gray, and black outside of the ellipse is an intuitively reasonable result. Because these neutral colors have special lightness, which can be much higher than, much lower than, or exactly the same as the background, some effect of lightness difference caused a stronger impression than colors in the hue circle.

B. Comparison of Data from Two Experiments

We performed two kinds of experiments in this study: word impression evaluation by hue and color impression evaluation by the SD method. The subject task should be processed by several different neural systems: not only by the visual information processing system but also by verbal communication and language processing systems in combination with a decision-making system, at least. Nevertheless, the data from these two experiments are mathematically symmetric in terms of the PCA. In traditional studies [6–8], since only experimentation using the SD method was performed, it would be of little use to try the other PCA in the other direction of analysis using a transposed matrix of the data, since these two sets of results are mathematically identical. In this study, however, we performed two experiments and obtained two sets of data independently. Thus, in this section, we compare the distribution of hues (colors) and the distribution of semantic words in the two sets of experimental results.

We would like to mention two factors that may influence the comparison. One factor is the data structure of the PCA. It was generally found that the structure of items in the distribution of the loading values would have structure with less distortion than that in the distribution of the score values, since the subjects had to think about the balance of color selection and semantic word selection. Thus, in the loading values, all selective items would be balanced in the subject’s performance. Conversely, words evaluated by hues and colors evaluated by semantic words were presented once at the set of trials and once in the session. This means that for the subject it was difficult to think about the balance of evaluative items; this may have distorted the structure of items in the score values.

The other factor that could have affected the results is the fact that in the color-paired comparison method, the subject looked at colors only briefly because the task was a much simpler one, responding left or right, than determining numerical grades for 35 semantic words for one color. The average times for one trial in the color-paired comparison method and the SD method were roughly 4 s and 8 min, respectively. In terms of chromatic flash processes, 4 s is sufficient time compared to the chromatic impulse response [19,20]. It is known, however, that in terms of color constancy effect the appearance of color might be affected by chromatic adaptation [1,21].

In a comparison of color distribution for the two sets of results shown in Figs. 7 and 10, the difference could be explained by the above two factors. We would like to mention, however, that some colors were stable in the structure comparison but others were not; antagonistic relationships in the hue circle were basically kept in yellowish-orange (v6) and blue (v18) and in green (v12) and red-purple (v24). However, the antagonistic relationships commonly used were not stable in red (v2) and blue-green (v14) and in yellow (v8) and violet (v20). The reason for this difference has not been clearly determined; three new colors (white, gray, and black) were measured independently in a different session in the SD method and should not have distorted the color distribution. Further experiments are needed to investigate the stability of colors in the evaluation process.

In order to compare the semantic word distributions in the two sets of results shown in Figs. 8 and 9, we transformed the data of Fig. 8 by linear expansion (compression) and rotation of each axis of Fig. 8 separately. We plotted that transformed data in Fig. 11 with the data of Fig. 9 (the core nine words only). In Fig. 11, the optimized weight values for the first PC and the second PC were compressed by a factor of 0.269 and 0.787, respectively, and the axes were rotated $-12.2$ and 140.3 deg, respectively, in order to minimize the sum of the distances between data points of the two sets of results for each semantic word. If the distance between corresponding points for the two sets of results was larger than the average, the two points were connected by dotted line. As shown in Fig. 11, some words are robust for different methods of measurement; the distances for “visible,” “vigorous,” “extreme” and “massive” were small, suggesting that these semantic words can easily be described by hues. Conversely, the distances for “tranquil,” “magnificent,” “deserted” and “fine” were large, suggesting that it is not so suitable to describe semantic words by hues; we can imagine that it was rather difficult for the subjects to select hues for these words.

Interestingly, the comparison between the results of evaluation of word impression by hue and evaluation of color impression by the SD method reveals which colors (hues) are suitable for expressing word impressions and which words are suitable for expressing color impression. Thus, colors and words can be classified using this methodology in terms of color-concept association. The ranking of the relationship between colors and words may reveal a mechanism of evaluation processes in the human brain, consisting of the visual information processing system and verbal communication and language processing systems in combination with a decision-making system, at least. Further investigation using brain measurements is expected to confirm this point; it will be possible to investigate the process of color-concept association in these processing systems using differences of brain activities measured by fMRI between these different tasks and between strong and weak associations.

5. CONCLUSION

We investigated the semantic word impression expressed by hue using the color-paired comparison method. A linear model using two main principal components can predict the modified selection rates of hue selection. In the process expressing semantic word impression by hue, these hues are treated as a hue circle, rather than categorical colors. Comparison of the results for evaluation of semantic words by hue and for evaluation of hues by semantic words suggests that suitability for evaluation is different for words and colors.

Two categories of semantic words were found to be stable in this study: one is “visible,” “vigorous,” and “extreme,” and the other is “clean” and “massive.” The words “tranquil,” “magnificent,” “deserted,” and “fine” are not necessarily suitable for evaluation or for use in the evaluation of hue because the results of measurements in different directions did not match well. Similarly, hues varied in suitability for evaluation; antagonistic relationships in the hue circle were basically kept in yellowish-orange (v6) and blue (v18) and in green (v12) and red-purple (v24), but the commonly used antagonistic relationships were not so stable in red (v2) and blue-green (v14) and in yellow (v8) and violet (v20). Further research is required to investigate the stability of words and colors, especially in the case of three-dimensional chromatic stimulations.