A book what I readed

“The grammar of graphics determines how algebra, geometry, aesthetics, statistics, scales and coordinates interact”

Variables

Operations applied before scale transformations

• Mathematical transforms (sin, log)
• Sorting and ranking
• Aggregation
• Quantiles
• Residuals

Algebra

Let \(A := (x,y,z)\) and \(B := (a,a,b)\)

• Cross, \(A\times B\) \[ = ([x,y],~[y,a],~[z,b]) \]

• Nest, \(A/B\)
  \[ = (x|a,~y|a,~z|b) \]

• Blend, \(A+B\) \[ = (x,y,z,a,a,b) \]

Scales

• Categorical
• Interval
• Time
• One-bend (log, power)
• Two-bend (arcsine, logit, probit)
• Probability

“Graphics do not care about the scales on which they are drawn”

Scales

Statistics

After scale & variable transformations
Before coordinate transformations

• Regression coefficients
• Smoothers
• Binning and aggregation
• Confidence intervals
• Density estimation

Geometry

Things we can actually see

Collision modifiers: stack, dodge, jitter

Coordinates

“Ordinary graphics such as intervals and polygons take on radically different appearances under different planar transformations.”

• Cartesian coordinates
• Triangular coordinates
• Polar coordinates
• Map projections
• Conformal mapping

Coordinates

A new graphic? Or a transformation of an existing one?

Aesthetics

“Much of the skill in graphic design is knowing what combinations of attributes to avoid.”

Let’s make a pie chart

Titanic dataset

head(Titanic)

##   Class    Sex   Age Survived Freq
## 1   1st   Male Child       No    0
## 2   2nd   Male Child       No    0
## 3   3rd   Male Child       No   35
## 4  Crew   Male Child       No    0
## 5   1st Female Child       No    0
## 6   2nd Female Child       No    0

Algebra: Class × Survived × Freq

Let’s make a pie chart

pie <- ggplot(Titanic) +
  scale_x_discrete() + scale_y_continuous() + scale_fill_discrete() +
  geom_bar(width = 1, position = "fill") +
  aes(x = "", fill = Survived, weight = Freq) +
  theme_titanic()

Let’s make a pie chart

pie <- pie + coord_polar(theta = "y")

Let’s make a pie chart

pie <- pie + facet_grid(. ~ Class)

Let’s make a pie chart

Napoleon’s March

Napoleon’s March

gg <- ggplot(troops, aes(x = long, y = lat))
gg <- gg + geom_path(aes(size = survivors,
                         colour = direction,
                         group = group), lineend = "round")
gg <- gg + geom_text(data = cities, aes(label = city),
                     size = 3, family = "serif", fontface = "italic")

Napoleon’s March

Implementations

• Graphics Production Language (SPSS)

• ggplot2 / ggvis (R)

• Bokeh (Python)

• Gadfly (Julia)

• D3 / Vega (JavaScript)

• Grammarphone (Spotify API)

Asciiplot

source('asciiplot.R')
asciiplot(df = iris,
          aes = list(x='Sepal.Width', y='Sepal.Length'),
          geom = 'point')

##                                                     O                     
##                   O   O     O                       O                     
##                             O                                             
##                       O                                                   
##                           O O       O           O                         
##                             O                                             
##                                 O   O                                     
##                       O     O       O                                     
##               O           O O   O     O                                   
##                       O     O       O                                     
##         O     O     O O   O     O   O O O                                 
##       O               O   O             O                                 
##       O           O O O   O O           O                                 
##                             O       O                                     
##               O   O O O   O O                       O     O             O 
##               O     O O   O O                                             
##         O O   O   O         O           O   O     O     O         O       
##                                                   O                       
##               O     O                 O O   O     O O         O           
## O       O O   O             O   O   O O O   O   O                         
##                             O   O       O                                 
##                                     O                                     
##         O                       O   O   O       O                         
##                           O O       O                                     
##                             O

Grammarphone

• Implements a sound geom for line graphs

• Maps values in data to frequency/volume of music

• Awarded 1st prize at Anvil Hack II

• Definitely useful

• Try it here

References

• Wilkinson, Leland. The Grammar of Graphics. 2nd edition. Springer Science & Business Media, 2005.

• Wickham, Hadley. “A layered grammar of graphics.” Journal of Computational and Graphical Statistics 19.1 (2010): 3–28.

Source code available on Github