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# color: beautiful

UCD Computational and Molecular Biology Symposium, Dublin, Ireland. 1-2 Dec 2016.

# visualization + design

Some of the images in this writeup are part of Ana Swanson's Wonk Blot post How a dog sees a rainbow, and 12 other images that explain how we see color at the Washington Post.

# Color Palettes for Color Blindness

In an audience of 8 men and 8 women, chances are 50% that at least one has some degree of color blindness1,2. When encoding information or designing content, use colors that is color-blind safe.

1About 8% of males and 0.5% of females are affected with some kind of color blindness in populations of European descent (wikipedia, Worldwide prevalence of red-green color deficiency, JOSAA). The rate for other races is lower Asians and Africans is lower (Caucasian Boys Show Highest Prevalence of Color Blindness Among Preschoolers, AAO).

2The probability that among $N=8$ men and $N=8$ women at least one person is affected by color blindness is $P(men,women) = P(8,8) = 1 - (1-0.08)^8 * (1-0.005)^8 = 0.51$. For $N=34$ (i.e., 68 people in total), this probability is $P(34,34)=0.95$. Because the rate of color blindness in women is so low, for most groups of mixed gender we can approximate the probability by only counting the men. For example, in a group of 17 women the probability that at least one of them is color blind is $P(0,17) = 0.082$, which is the same probability as for 1 man, $P(1,0)$.

Color Oracle is a good and free color blindness simulator for Windows, Mac and Linux.

## color blindness RGB transformation tables

You can download the RGB transformation table for deuteranopia, protanopia and tritanopia. It is available for all (r,g,b) colors in steps of 5 in each of the channels. The mapping for all other RGB colors can be interpolated.

Transformation for all 16.8 million RGB colors (interpolated from the table above) are also available independently for each type of color blindness: deuteranopia, protanopia, and tritanopia.

## color receptors are reduced or absent in color blindness

The normal human eye is a 3-channel color detector3. There are three types of photoreceptors, each sensitive to a different part of the spectrum. Their combined response to a given wavelength produces a unique response that is the basis of the perception of color.

3Compared to hearing, the color vision is a primitive detector. While we can hear thousands of distinct frequencies and process them simultaneously, we have only three independent color inputs. While the ear can distinguish pure tones from complex sounds that have multiple frequencies the eye is relatively unsophisticated in separating a color sensation into its three constituent primary stimuli.

People with color blindness have one of the photo receptor groups either reduced in number or entirely missing. With only two groups of photoreceptors, the perception of hue is drastically altered.

For example, in deuteranopia, the most common type of color blindness, the medium (M) wavelength photoreceptors are reduced in number or missing. This results in the loss of perceived difference between reds and greens because only one group of photoreceptors (L) are sensitive to the wavelengths of these colors. The spectrum appears to be split into two hues along the blue-green boundary (see figure below).

Each of the three kinds of color blindness are associated with reduced number of each of the three kinds of photoreceptors. In extreme cases, a given type of photoreceptors may be missing. To people with color blindness, objects appear very differently. Artwork is (left) Edvard Munch, Scream (Skrik), 1893, National Gallery, Oslo, Norway (right) Claude Monet, Coquelicots, La promenade (Poppies), 1873, Musée d'Orsay, Paris. (zoom)

Visible light is in the range of 390-700 nm. The exact definition of the upper limit varies, with some sources giving as high as 760 nm. Shorter wavelengths are absorbed by the cornea (<295nm) and lens (315-390nm). Some near infrared light also reaches the retina (760-1400nm).

## super color vision

The opposite condition to color blindness exists too—tetrachromacy. In this case, an individual has an extra type of color receptor which improves discrimination in the red part of the spectrum. While the anatomy of their retina can be described, how true tetrachromats subjectively perceive color is unknown. And, perhaps, even unknowable.

Tetrachromacy is common in other animals, such as fish (e.g. goldfish, zebrafish) and birds (e.g. finch, starling). The dimensionality of the perceived color space isn't necessarily proportional to the number of different receptors. If the signal from 3 color receptors are combined by the brain and each processor has a weighted response to a broad range of wavelengths, then a color can be modeled by a point in 3-dimensional space, in which the receptors are the axes. This system can perceive a large number of colors.

In the extreme case where the receptors respond to a very narrow range, of which none overlap with the other, a color is one of three points in a 1-dimensional space. This sytem can perceive only 3 colors.

For example, although the mantis shrimp has 12 different color receptors, the receptors work independently, their color discrimination is poorer than ours.

## it's all the same to me

Sets of representative hues and tones that are indistinguishable to individuals with different kinds of color blindness. The rectangle below the each color pair shows how the colors appear to someone with color blindness.

If you use Color Oracle to transform your screen colors to simulate color blindness, you can see that none of the equivalent swatches in one kind of color blindness are equivalent in another. This is particularly interesting when applied to a duotone image which is drawn using equivalent colors. In the figure below4, a row of Mr. Spocks disappears (or is difficult to see) to people with color blindness.

The likeness of Mr. Spock drawn using equivalent colors (see image above) for each of the three kinds of color blindness. Image from imagebuddy.

4In tribute to Leonard Nimoy, 1931–2015

## conservative 7-color palettes for color blindness

To people with color blindness, some colors appear the same. This equivalence can be used to identify distinct colors which are unique to those with normal and color blind vision.

The seven colors (and black) in the figure below are perceived as reasonably distinct by both normal and color blind individuals. The table on the left is reproduced from Nature Method's Points of View: Color blindness by Bang Wong.

(left) 7-color palette for color blindness, from Wong, B. (2011) Nature Methods 8:441. (right) The same palette ordered by hue and tone for a deuteranope. (zoom, PDF)

For more tips about designing with color blindness in mind, see Color Universal Design (CUD) — How to make figures and presentations that are friendly to Colorblind people.

## 12-color palettes for color blindness

The figure below shows the mapping of different colors to six different grades of each of the two hues seen by deuteranopes. It offers more distinct options than the 7-color palette above.

(left) Colors grouped by equivalence of perception in deuteranopes. Each of the two hues is represented in six different brightness and chroma combinations. (right) One of the subsets of colors on the left that are reasonably distinct in both deuteranopia and protanopia. To tritanopes, three of the pairs are difficult to distinguish. (zoom, PDF)

## 15-color palettes for color blindness

Even more color choices for color blindess, including colors that map onto greys.

If you're looking to encode quantitative information, I suggest using the subset of Brewer palettes that are safe for color blindess (e.g. pink-yellow-green, brown-blue-green).

15-color palettes designed for each of the three types of color blindness: deuteranopia, protanopia and tritanopia. Palettes are shown as they appear to someone with normal vision as well as to someone affected with each of the three types of color blindness. Each palette contains three groups of swatches, matching to two of the color channels and greys. Within each group colors in the same row map onto the same color. (zoom, PDF)
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# Intuitive Design

Thu 03-11-2016

Appeal to intuition when designing with value judgments in mind.

Figure clarity and concision are improved when the selection of shapes and colors is grounded in the Gestalt principles, which describe how we visually perceive and organize information.

One of the Gestalt principles tells us that the magenta and green shapes will be perceived as as two groups, overriding the fact that the shapes within the group might be different. What the principle does not tell us is how the reader is likely to value each group. (read)

The Gestalt principles are value free. For example, they tell us how we group objects but do not speak to any meaning that we might intuitively infer from visual characteristics.

Nature Methods Points of View column: Intuitive Design. (read)

This month, we discuss how appealing to such intuitions—related to shapes, colors and spatial orientation— can help us add information to a figure as well as anticipate and encourage useful interpretations.

Krzywinski, M. (2016) Points of View: Intuitive Design. Nature Methods 13:895.

# Regularization

Fri 04-11-2016

Constraining the magnitude of parameters of a model can control its complexity.

This month we continue our discussion about model selection and evaluation and address how to choose a model that avoids both overfitting and underfitting.

Ideally, we want to avoid having either an underfitted model, which is usually a poor fit to the training data, or an overfitted model, which is a good fit to the training data but not to new data.

Nature Methods Points of Significance column: Regularization (read)

Regularization is a process that penalizes the magnitude of model parameters. This is done by not only minimizing the SSE, $\mathrm{SSE} = \sum_i (y_i - \hat{y}_i)^2$, as is done normally in a fit, but adding to this minimized quantity the sum of the mode's squared parameters, $\mathrm{SSE} + \lambda \sum_i \hat{\beta}^2_i$.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Regularization. Nature Methods 13:803-804.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Model Selection and Overfitting. Nature Methods 13:703-704.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Classifier evaluation. Nature Methods 13:603-604.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Logistic regression. Nature Methods 13:541-542.

# Model Selection and Overfitting

Fri 04-11-2016

With four parameters I can fit an elephant and with five I can make him wiggle his trunk. —John von Neumann.

By increasing the complexity of a model, it is easy to make it fit to data perfectly. Does this mean that the model is perfectly suitable? No.

When a model has a relatively large number of parameters, it is likely to be influenced by the noise in the data, which varies across observations, as much as any underlying trend, which remains the same. Such a model is overfitted—it matches training data well but does not generalize to new observations.

Nature Methods Points of Significance column: Model Selection and Overfitting (read)

We discuss the use of training, validation and testing data sets and how they can be used, with methods such as cross-validation, to avoid overfitting.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Model Selection and Overfitting. Nature Methods 13:703-704.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Classifier evaluation. Nature Methods 13:603-604.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Logistic regression. Nature Methods 13:541-542.

# Classifier Evaluation

Tue 13-09-2016

It is important to understand both what a classification metric expresses and what it hides.

We examine various metrics use to assess the performance of a classifier. We show that a single metric is insufficient to capture performance—for any metric, a variety of scenarios yield the same value.

Nature Methods Points of Significance column: Classifier Evaluation (read)

We also discuss ROC and AUC curves and how their interpretation changes based on class balance.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Classifier evaluation. Nature Methods 13:603-604.