Understanding 'Scale' in R

Understanding `scale` in R

log simply takes the logarithm (base e, by default) of each element of the vector.

scale, with default settings, will calculate the mean and standard deviation of the entire vector, then "scale" each element by those values by subtracting the mean and dividing by the sd. (If you use scale(x, scale=FALSE), it will only subtract the mean but not divide by the std deviation.)

Note that this will give you the same values

   set.seed(1)
   x <- runif(7)

   # Manually scaling
   (x - mean(x)) / sd(x)

   scale(x)

Understanding color scales in ggplot2

This is a good question... and I would have hoped there would be a practical guide somewhere. One could question if SO would be a good place to ask this question, but regardless, here's my attempt to summarize the various scale_color_*() and scale_fill_*() functions built into ggplot2. Here, we'll describe the range of functions using scale_color_*(); however, the same general rules will apply for scale_fill_*() functions.

Overall Categorization

There are 22 functions in all, but happily we can group them intelligently based on practical usage scenarios. There are three key criteria that can be used to define practically how to use each of the scale_color_*() functions:

1. Nature of the mapping data. Is the data mapped to the color aesthetic discrete or continuous? CONTINUOUS data is something that can be explained via real numbers: time, temperature, lengths - these are all continuous because even if your observations are 1 and 2, there can exist something that would have a theoretical value of 1.5. DISCRETE data is just the opposite: you cannot express this data via real numbers. Take, for example, if your observations were: "Model A" and "Model B". There is no obvious way to express something in-between those two. As such, you can only represent these as single colors or numbers.

2. The Colorspace. The color palette used to draw onto the plot. By default, ggplot2 uses (I believe) a color palette based on evenly-spaced hue values. There are other functions built into the library that use either Brewer palettes or Viridis colorspaces.

3. The level of Specification. Generally, once you have defined if the scale function is continuous and in what colorspace, you have variation on the level of control or specification the user will need or can specify. A good example of this is the functions: *_continuous(), *_gradient(), *_gradient2(), and *_gradientn().

Continuous Scales

We can start off with continuous scales. These functions are all used when applied to observations that are continuous variables (see above). The functions here can further be defined if they are either binned or not binned. "Binning" is just a way of grouping ranges of a continuous variable to all be assigned to a particular color. You'll notice the effect of "binning" is to change the legend keys from a "colorbar" to a "steps" legend.

The continuous example (colorbar legend):

library(ggplot2)
cont <- ggplot(mtcars, aes(mpg, disp, color=cyl)) + geom_point(size=4)

cont + scale_color_continuous()

The binned example (color steps legend):

cont + scale_color_binned()

The following are continuous functions.

facet_wrap(reformulate("Name","."), scales = 'free', nrow = 1) +

x <- runif(1000)  # symmetric around 0.5
y <- rexp(1000)  # not symmetric around 1 at all

summary(scale(x))
summary(scale(y))

## Data to make a minimal reproducible example
m <- matrix(rnorm(9), ncol=3)

## Rescale each column to range between 0 and 1
apply(m, MARGIN = 2, FUN = function(X) (X - min(X))/diff(range(X)))
#           [,1]      [,2]      [,3]
# [1,] 0.0000000 0.0000000 0.5220198
# [2,] 0.6239273 1.0000000 0.0000000
# [3,] 1.0000000 0.9253893 1.0000000