Analyzing and predicting colour preference of colour palettes

Abstract

A palette composed of multiple colour patches can express lots of information. This study aimed to explore the factors that influenced colour palette preference, including colour attributes and colour differences between colour patches. A new attribute called Delta_Order for calculating the colour difference of a palette was presented, which fully considered the colour difference and the placement. In order to comprehend colour palette preference intuitively, a prediction model of palette preference was proposed based on lightness, chroma and the new metric Delta_Order. Two psychophysical experiments including analyzing and validating experiments were conducted. Fifty observers were invited to evaluate the colour palette preference. The results indicated that lightness played an important role in colour preference, but colour preference was not related to hue angle. For Delta_Order, there was a significant negative correlation between the new metric and preference score since the Pearson correlation coefficient was −0.801. This meant that observers preferred the palettes with low Delta_Orders. According to the validating test, it confirmed that the proposed prediction model had a good stability. The predicted trends were consistent with the true results, and the scores were similar to each other. These analysis results had a certain guiding significance in design and industry about colour.

1. Introduction

Colour preference refers to which colour individuals prefer. It has been actively researched for a long time. Also, it plays an important role in many fields including consumption, design and industry [[1], [2], [3], [4], [5], [6]]. Colour preference is related to colour attributes, and it can be impacted by individual preference and the conditions of observation [[7], [8], [9], [10], [11]]. Colour attributes are generally represented by lightness ($L^{*}$), chroma ($C_{ab}^{*}$) and hue ($h_{ab}$). Different colours can be accurately identified and distinguished from each other by the three attributes. Lightness is a measure of the luminous intensity of the light reflected from the surface of a colour object; chroma, also called ‘saturation’, describes how vivid colour is; hue is identified as how most of us name a colour, such as red, green, blue, yellow, etc. Some studies [8,12,13] investigated the effect of colour attributes on preference. It was proven that lightness was one of the important factors affecting colour preference. For example, the record of skin conductance and electrocardiogram illustrated that lightness had a significant effect on one's emotion [12]. Moreover, light colours were preferred among Chinese adults [14]. In terms of hue preference, many researches suggested that most of people preferred blue to yellow and green [[15], [16], [17]]. Furthermore, some researches focused on the influence of gender [18,19], age [20,21] and culture [6,22].

In recent years, colour has been more comprehensively expressed with the emergence of colour palettes [23]. A colour palette consists of a series of colour patches. The information contained in colour palettes is exceedingly abundant, and various collocations reflect different emotions. It is generally believed that colour collocations directly affect purchase choices for different products [24,25]. Different colour matching experiments have been reported to accomplish a humanized industrial design including car interior design [26], UI design of social software [27], interior design exhibition [28] and so on, since colour is a vital part of the product in industrial design. A number of digital tools, including the Adobe Colour website [29], Colourmind [30] and so on, have been employed to generate colour palettes automatically. Moreover, palette-based image recoloring has attracted attention in recent years [31]. Researchers tackled the recoloring problem with various approaches and purposes [32,33]. Chang and Fried [32] improved the K-means method to attain the palettes from images. Furthermore, they designed a novel colour transfer algorithm that recolored the image using the palettes. Bahng and Yoo [33] proposed a deep neural network architecture which could generate multiple colour palettes based on the input text and then used the generated palettes to recolor a grey image.

Except for the methods of generating and using colour palettes aforementioned, colour harmony formulae to describe observers' impressions of colour harmony for colour combinations have also been investigated in many literatures [[34], [35], [36]]. In Ref. [35], based on the correlations among hue, chroma, and lightness of colour patches, colour harmony formulae were developed to predict colour harmony. Colour difference refers to the difference of visual perception between two colour samples. At present, CIE DE2000 formula is widely used [37]. Several scientists paid attention to colour differences between palettes and then tried to predict visual similarity among palettes. Pan proposed [36] three different models named Single Colour Difference Model, Mean Colour Difference Model, and Minimum Colour Difference Model, respectively. These models could measure colour differences between palettes. As a result, the Minimum Colour Difference Model was most effective. However, the experiment designed by Pan focused on the palettes with a larger number of colour patches. To verify the rationality of the Minimum Colour Difference Model in palettes with a smaller number of colour patches, another experiment was carried out by Yang et al. to measure the similarity between palettes with five colour patches placed horizontally [38]. The conclusion was the same as Pan's. Ren et al. [39] were concerned with predicting visual self-similarity for colour palettes with a large number of patches. The predictions of Pearson Correlation Coefficient method were considered to have a good agreement with the visual data. Previous studies indicated that the colour differences between colour patches affected the observer's judgment of the similarity of palettes. However, there were few studies on the correlation between colour differences and palette preference, so colour differences should be further explored for a deeper understanding of palette preference.

In summary, this study focuses on exploring the influencing factors of palette preference. Thus, three hypotheses are proposed.

Hypothesis 1

Lightness of a palette will affect palette preference.

Hypothesis 2

The order of colour patches composing a palette will affect palette preference.

Hypothesis 3

The colour differences between colour patches composing a palette will affect palette preference.

The current study aims to investigate the factors that influence palette preference and set a model to predict the preference scores. In two psychophysical experiments, analysis and validation are conducted, respectively. 100 palettes with various colour patches are selected as the experiment objects. A metric called Delta_Order related to colour differences between colour patches is proposed. Three attributes including lightness, chroma and the new metric Delta_Order are used to design a palette preference prediction model. In addition, other 40 palettes are randomly chosen to test the accuracy of the model. More information about the used colour palettes is available at https://drive.google.com/drive/folders/1G2_fdJSuLk4yP5Mh4GtZRcSamf-o5cys?usp=share_link.

2. Method

2.1. Colour palettes preparation

A total of 90 palettes were obtained from a series of images. These palettes were carefully selected. The distribution of colours consisting of the palettes is as large as possible in the color space, and the colour palettes had various hue, chroma and lightness. All the palettes contained six colour patches arranged in row. Fig. 1 shows the distribution of colours composing the palettes in CIE $L^{*}{a}^{*}{b}^{*}$ space, where each dot represents a colour patch.

Fig. 1.

Colour distribution of all patches in palettes: (a) colour distribution of all patches in $a^{*}{b}^{*}$ colour space, (b) colour distribution of all patches in $L^{*}{C}_{ab}^{*}$ colour space, (c) colour distribution of all patches in $L^{*}{a}^{*}$, and (d) colour distribution of all patches in $L^{*}{b}^{*}$ colour space. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

To investigate whether the order of colour patches in colour palettes impacted the preference result, 7 palettes were randomly selected among the 90 palettes, and colour patches in each of the 7 palettes were rearranged in a different order to get a palette pair. An example of a palette pair is shown in Fig. 2.

Fig. 2.

One pair of palettes with the same patches in different orders: (a) a palette of the palette pair, and (b) the other palette of the palette pair.

Further, three palettes were randomly chosen from 90 palettes, and these palettes were used two times in the psychophysical experiment to ensure the repeatability of the observers. That is to say, in total, there were 100 palettes for the psychophysical experiment.

After analyzing palette preference, a prediction model for predicting palette preference was designed. To verify the correctness of the model, another set of 40 palettes was also obtained from a series of images.

2.2. Experimental design

A total of thirty-nine observers including nineteen males and twenty females were invited to participate in palette preference test. Participants signed an informed consent form to agree to their participation. Their ages ranged from 18 to 26. All of them passed Ishihara's test for colour deficiency. A validation test was set after completion of analysis experiments. There were other eleven observers who attended the validation test in two weeks. The study was accomplished by maintaining the ethical concerns of the research. This study was approved by the Research Center of Graphic Communication, Printing and Packaging, Wuhan University.

The palette preference test was carried out on Intelli Proof 244 ex (QUATO, Germany; 102% NTSC wide gamut proof monitor). It was calibrated via a spectrophotometer X-Rite i1 Pro and the colour management software ProfileMaker 5.0. Several parameters including colour gamut, correlated colour temperature and luminance were set to be sRGB, 6,500 K and 120 cd/m², respectively. Fig. 3 shows the user interface of the test. The palettes were shown in a random sequence and displayed on a neutral grey background.

Fig. 3.

User interface of the experiment.

In the experiment, each participant was requested to evaluate the degree of palette preference. A seven-point rating method was used to score palette preference. The degree of palette preference was set on a scale of 1–7, ranging from ‘strongly dislike’ to ‘strongly like’. Meanwhile, 4 represented to be neutral.

2.3. Experimental procedure

The palette preference experiment was carried out in a dark room. Firstly, each observer was asked to implement the Ishihara Colour Vision Test once he or she got ready to start. Each observer was required to wear a grey coat in order to avoid other reflectance during testing. Then, they adjusted the chair and sat at a proper distance until the palette in the middle of the monitor was seen clearly. After the preparation, they stared at a neutral grey screen (128, 128, 128) about 3 min to adapt to the dark environment.

At the beginning of the test, all the 100 palettes were presented to each observer to make him or her have an overall impression. After displaying these palettes, there was a procedure to familiarize the observers with the experiment process, especially the user interface operation.

In the scale rating process, each observer was asked to assess each palette based on their personal preference. They clicked the button on the UI to rate each palette. All the palettes were shown to the observers in a random order, and all the observers did not know the intention of the experiments, which could reduce the limitations of memory and attention at most. After all palettes were evaluated, the entire colour palette preference experiment was completed. For each participant, the whole experiment took about 30 min.

Two weeks later, a further 11 observers (who did not take part in the first experiment) were invited to evaluate 40 palettes to validate the prediction model. Two experimental procedures were similar. The validation experiment lasted about 10 min.

3. Result and discussion

3.1. Observer variability

As aforementioned, to ensure the stability of the observers, three palettes were randomly chosen from 90 palettes and used two times during the preference test. During verifying the intra-observer variability, the absolute-difference method is used [10,11]. Two responses whose absolute difference is more than two for the same palette are defined as an abnormal data pair, and then the ratio of the abnormal data pairs to the total number of repeated data pairs is calculated. In this work, the intra-observer stability of palette preference is 6.18%. The result of this intra-observer variability is similar to the study of colour preference under different lighting conditions [10].

To verify the consistency of answers between different observers, the inter-observer variability of palette preference is determined by the Coefficient of Variation (CV). The formula of CV in this work is shown as Eq. (1).

$$CV=\frac{{\left[\sum _{i=1}^n{\left(x_i-\bar{x}\right)}^2/n\right]}^{1/2}}{\bar{x}}$$ (1)

where $x_i$ represents an observer's response about the $i$ palette; $\bar{x}$ represents the mean value of all the observers' responses for one palette; $n$ is the total number of observers in the test. The lower the CV value, the more the observers agree with each other, and the more effective the experimental data. The average inter-observer variance of this test is 32.79. The value of CV in this test is reasonable compared with the result from Pan [36] focusing on palette similarity, which indicates that the inter-observer variability is stable.

3.2. The effect of colour properties

Different palettes are composed of different colour patches, which have a wide range of colour attributes. To determine which colour attribute affectes palette preference, we first take three appearance attributes, lightness, chroma and hue into consideration [40]. To be noted, each colour attribute value of each palette is defined as the accumulated value of the corresponding colour attribute values for all colour patches constituting the palette.

The Pearson correlation coefficients (PCCs) between the preference ratings and colour attributes ($L^{*}$, $C_{ab}^{*}$, $h_{ab}$) are calculated, and the results are 0.699, −0.564, and 0.086 for $L^{*}$, $C_{ab}^{*}$, $h_{ab}$, respectively. It is clear that lightness and chroma are significantly correlated with palette preference, while the cumulative value of hue is nearly not correlated with preference. Specifically, lightness is positively correlated with preference, and chroma is negatively correlated with palette preference. It indicates that average observers prefer palettes with higher lightness and lower chroma, and the hue of the palettes does not correlate with average preference of observers.

To understand the interaction between colour attributes and palette preference better, analysis of variance (ANOVA) is performed. Firstly, the conditions of ANOVA test are verified. Kolmogorov-Smirnov (K–S) index is used to test the normality, and Levene index is used to test homogeneity of variance. The significance value of K–S test is greater than 0.05. The Levene's test of equality of error variances based on mean value is 0.205 which is larger than 0.05. Therefore, it fits the premise of the analysis of variance.

Table 1 shows the results of ANOVA test. It indicates that lightness and chroma significantly affect palette preference (Sig < 0.05). The hue of palette has no significant influence on palette preference. As can be seen, there is no interaction effect between any two independent variables for palette preference, so the effects are mainly from lightness and chroma. The metric Partial Eta Squared (${\eta }_p^2$) [41] is chosen to quantify the effect size of these two factors. It is clear that the most important influencing factor is lightness followed by chroma in terms of ${\eta }_p^2$. Meanwhile, hypothesis 1 is verified.

Table 1.

Analysis of variance about the effect of the $L^{*}$, $C_{ab}^{*}$, $h_{ab}$.

Independent variable	SS	Df	MS	F	Sig	${\eta }_p^2$
$L^{*}$	12.429	3	4.143	11.562	.000	0.374
$C_{ab}^{*}$	8.899	4	2.225	6.209	.000	0.300
$h_{ab}$	0.092	4	0.023	0.064	0.992	0.004
$L^{*}$& $C_{ab}^{*}$	2.240	6	0.373	1.042	0.408	0.097
$L^{*}$& $h_{ab}$	3.026	6	0.504	1.407	0.227	0.124
$C_{ab}^{*}$& $h_{ab}$	5.810	8	0.726	2.027	0.059	0.218

SS: sum of squares; MS: mean square.

The results of the residual analysis are shown in Fig. 4. Fig. 4(a) indicates the frequency of standardized residual. It can be seen that it meets normal distribution and most residual values range between −2 and 2. Through the analysis of residual distribution in Fig. 4(b), it is clear that the values are distributed on both sides of the x-coordinate uniformly.

Fig. 4.

The results of residual analysis. (a) The frequency of standardized residual, and (b) the analysis of residual distribution.

3.3. The effect of order

Colour difference is widely used for colour evaluation and is also related to the human vision. Therefore, colour differences between colour patches are taken into account. In this work, the colour difference formula CIE DE2000 is used.

Multiple colour patches constituting a colour palette can be arranged in various ways when placed horizontally [38]. To further investigate the correlation between palette preference and the order of the patches, seven pairs of palettes which have the same colours with the different orders are used.

Fig. 5 visualizes the colour differences of palettes by calculating the sum of colour differences between the adjacent colour patches and colour difference between the first and the last colour patch of palettes. Specifically, colour patches are labelled by ‘1’, ‘2’, ‘3’, ‘4’, ‘5’ and ‘6’, respectively. Colour differences between ‘1’ and ‘2’, ‘2’ and ‘3’, ‘3’ and ‘4’, ‘4’ and ‘5’, ‘5’ and ‘6’, ‘1’ and ‘6’ are computed. Then, all the computed colour differences are summed to represent the accumulative colour difference for the palette. As shown in Fig. 5, the rating results for each pair of palettes are completely inconsistent. It confirms that the order of placement affects palette preference. For each pair of colour palettes, the palette which has a higher accumulative colour difference has a lower score than the other palette. Therefore, it can conclude that for the colour palettes, the larger the accumulative colour differences, the lower the ratings. This result is reasonable because the palettes with large accumulative colour differences break the colour harmony. A strong visual perception usually discomforts observers. It proves that observers prefer palettes with less colour differences between adjacent colour patches.

Fig. 5.

The analysis of the effect of order.

To further verify that the order of colour patches can affect the palette preference, the correlations of accumulative colour differences and ratings are investigated. Firstly, the accumulative colour differences for 100 palettes are calculated. Then, the Pearson correlation coefficient (PCC) between the colour differences and the ratings accurately demonstrates the negative correlation (r = −0.738, Sig < 0.001). It is clear that palette preference is highly correlated to the colour placement and observers prefer palettes with less colour differences. Through the above analysis, we can conclude that the order of colour patches can affect personal preference, which is consistent with Hypothesis 2.

3.4. The effect of the new colour difference metric Delta_Order

Some new attributes have been proposed in previous literature on colour preference, but most of them are concerned with the single colour patch [1]. A few researches have focused on the colour differences between the palettes [38]. According to the analysis of preferred palettes, it is found that observers like the palettes with similar colours. To better illustrate the colour preference of the palette, based on the data obtained from this study, a novel metric called Delta_Order is proposed to quantify colour difference of the palette. This new parameter takes the colour difference and the order of the colour patches into consideration. Each colour patch in the palette is numbered as ‘1’, ‘2’, ‘3’ … ‘6’ from left to right in succession. The new metric can be achieved by the following five steps.

Firstly, starting with the colour patch ‘1’, the colour differences between the colour patch ‘1’ and all the colour patches on the right of colour patch ‘1’ are calculated. The sum of all colour differences about patch ‘1’ is called DE_1.

Secondly, step 1 is repeated for all the colours on the palette. The results are recorded as DE_2, DE_3, DE_4, DE_5 and DE_6. For example, DE_2 is the sum of colour differences between the pair of colour patch ‘2’ and ‘3’, the pair of ‘2’ and ‘4’, the pair of ‘2’ and ‘5’, the pair of ‘2’ and ‘6’.

Next, add up the DE_1, DE_2 … DE_6. The result is symbolized as DE_All.

Then, the colour differences between the pair of colour patch ‘1’ and ‘2′, the pair of ‘2’ and ‘3’, the pair of ‘3’ and ‘4’, the pair of ‘4’ and ‘5’, the pair of ‘5’ and ‘6’, the pair of ‘6’ and ‘1’ are calculated, and add them to get DE_Sequence. It is noted that the palettes with the same colour patches and different orders have the same DE_Alls, while the attribute DE_Sequences are discrepant. DE_Sequence focuses more on adjacent colour patches.

At last, add the DE_All and DE_Sequence to get the Delta_Order. The new metric Delta_Order representing the colour differences between colour patches fully considers the order of each colour patch.

The Delta_Orders of 100 palettes are plotted with the scores of the corresponding palettes, as shown in Fig. 6. The negative correlation of the two parameters is presented. We calculate the Pearson correlation coefficient between preference ratings and the Delta_Orders, and the Pearson correlation coefficient is −0.801, which illustrates that there is a powerful negative correlation between these two factors. Therefore, Hypothesis 3 is verified. Such results consolidate the finding that observers have a better sense to the patches with smaller colour difference to each other, which conforms to colour harmony theory.

Fig. 6.

Scatter diagram of the new metric Delta_Orders and the preference scores. The red line is the fitting curve. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

3.5. The accuracy of palette preference prediction model

It is essential to establish the connection between the attributes of palette and visual preference [7,17]. A prediction model is tried to predict the general preference of different colour palettes from the corresponding attributes. According to the correlation analysis of the palette mentioned above, there are the following findings: lightness has a significant influence on the preference; chroma is negative correlated with the ratings; there is a close correlation between Delta_Order and palette preference. Therefore, lightness, chroma and the proposed Delta_Order act as the input variables of the prediction method, and the visual score of palette preference act as the output variable.

In this work, multiple linear regression (MLR) is used as the prediction model since it can establish the relationship between the comprehensive response variable and two or more independent variables with simplicity and efficiency [42,43]. The model is stated as Eq. (2) [44].

$$Y={\beta }_0+{\beta }_1{X}_1+{\beta }_2{X}_2+\cdots +{\beta }_n{X}_n+\epsilon$$ (2)

where $X_1...X_n$ are the input variables including lightness, chroma and the Delta_Order, $Y$ is the preference score, ${\beta }_i$ is the regression coefficient, and $\epsilon$ is the stochastic error associated with the regression.

The least squares method (LSM) is used to obtain the estimation of regression coefficients within MLR [45]. LSM aims to search regression coefficients by minimizing the sum of error squares as Eq. (3).

$$\underset{{\beta }_0...{\beta }_n}{\mathit{min}}\parallel {\beta }_0+{\beta }_1{X}_1+{\beta }_2{X}_2+\cdots +{\beta }_n{X}_n-Y{\parallel }_2^2$$ (3)

To verify the accuracy of the prediction model proposed in this paper, a psychophysical experiment was carried out. In the psychophysical test, other 40 palettes were selected to be evaluated. Other eleven observers were invited to participate in this psychophysical experiment with the same process as the main experiment. These observers rated the preference of 40 palettes. At last, the 100 palettes were used for training the model, and the 40 palettes selected were used for testing the model.

Fig. 7 shows the predicted scores and the ground-truth scores of the validating test. In the upper part of Fig. 7, the red curve represents the predicted results of 40 palettes, and the blue one represents the ground-truth scores. It can be seen that the two curves have a consistent trend, which indicates that the results of subjective evaluation of the colour palettes by the prediction model have a high accuracy. Meanwhile, the lower part of Fig. 7 illustrates the differences between the two scores. It can be seen that most of the differences are within the range of −1 and 1. Especially, some of the differences are close to 0. The minimum difference between the two scores is 0.02 from Palette 34. The maximum difference between the two scores is 1.3 from Palette 19. It can be proved that the results obtained from this model are able to express personal preference of colour palettes.

Fig. 7.

Comparison with the predicted ratings and the ground-truth ratings. The error bars represent differences between them.

Three metrics, including Mean Absolute Error (MAE), Root Mean Squared Error (RMSE) and coefficient of determination (R-squared), are used to evaluate the performance of the prediction model. MAE and RMSE are set to calculate the absolute error and the root mean square error between the predicted value and the real value, respectively; R-squared is a statistical measure of how close the data is to the fitted line. These metrics are defined by Eqs. (4), (5), (6), respectively.

$$\mathrm{M}\mathrm{A}\mathrm{E}=\frac{\sum _{i=1}^n\left|\left({\bar{x}}_i-{\hat{x}}_i\right)\right|}{n}$$ (4)

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{\frac{\sum _{i=1}^n{\left({\bar{x}}_i-{\hat{x}}_i\right)}^2}{n}}$$ (5)

$${\mathrm{R}}^2=1-\frac{\sum _{i=1}^n{\left({\bar{x}}_i-{\hat{x}}_i\right)}^2}{\sum _{i=1}^n\left({\bar{x}}_i-\bar{x}\right)}$$ (6)

where ${\bar{x}}_i$ denotes the average response of each palette; $\bar{x}$ denotes the average response of all palettes; ${\hat{x}}_i$ denotes the corresponding predicted value; n denotes the total number of palettes.

To evaluate the accuracy and effectiveness of this method, the whole process of training and predicting repeated 100 times. In every time, we divided the total 140 palettes into training set and validation set randomly in a ratio of 8:2. The prediction errors for 100 times were averaged to get the final error of the MLR method, which could eliminate performance bias. At last, the average values of three metrics after 100 times are listed in Table 2. Specifically, MAE is 0.4826, RMSE is 0.5992, and R-squared is 0.5507. Compared with the possible MAE and RMSE ranging from 0 to 6, MAE and RMSE from the above are small enough. In addition, the regression analysis result (R-squared) is close to that of the PCC method from Ren [39], who thought that the PCC method could give the best agreement with the visual data. Therefore, the three measures illustrate that the multiple linear regression model presents a good performance in predicting colour palette preference.

Table 2.

The performance of the MLR prediction model.

Model	MAE	RMSE	R2
Preference Model	0.4826	0.5992	0.5507

Based on the above analysis about the influencing factors of palette preference, lightness, chroma and Delta_Order play a role in palette preference. This provides rational suggestions for the general public and designers in colour scheme, and makes it easier to choose proper colours.

4. Conclusion

In this paper, two sets of psychophysical experiments which aimed to acquire colour preference scores of colour palettes were carried out. We first studied the influence of different colour attributes on colour palette preference, including lightness, chroma and hue. In addition, the impact of the order of colour patches was also been considered. The following general colour harmony rules were found:

• (1)For colour palettes, higher lightness is preferred, and lower chroma produces better impressions. However, in the tested population, colour preference for hue does not show obvious consistency. The sum of hue for colour palette does not influence colour preference. The hue of the palettes does not correlate with average preference of observers.
• (2)Since different colour orders in colour palette generate different colour differences between adjacent colour patches, and large colour differences result in bad colour impression, colour orders for the colour combinations also have a great influence on colour preference.

Based on the analysis, a prediction model was developed. The results predicted by the model were consistent with those from the psychophysical experiments. Therefore, this model can be employed to evaluate all kinds of colour palettes.

These conclusions can provide suggestions for life, industry, consumption and other fields. The study results accentuate the benefits of suggesting the colour combinations to individuals without design experience when they select colours in daily life. The results also can guide commercial packaging design consciously, which may promote product sales.

Except for colour attributes, many other factors also have influences on colour preference. Therefore, further researches on colour emotion and colour harmony of colour palettes will be conducted.

Author contribution statement

Shuxin Yu: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data; Wrote the paper.

Lixia Wang: Analyzed and interpreted the data; Wrote the paper.

Yanhong Yang: Performed the experiments; Contributed reagents, materials, analysis tools.

Data availability statement

Data will be made available on request.

Declaration of interest's statement

The authors declare no conflict of interest.