• Data visualization is a core component of both exploring data and communicating results
• The goal: present data in a graphical way that shows patterns that are otherwise invisible
• Effective data visualization is challenging!
• No “gold standard” to follow - only principles and judgment

An effective data visualization:

1. Depicts accurate data
2. Depicts data accurately
3. Shows enough, but not too much, of the data
4. Is self contained - no additional information (except a caption) is required to understand the contents of the figure

A great visualization has some additional properties:

1. Exposes patterns in the data not easily observable by other methods
2. Invites the viewer to ask more questions about the data

• “Good plots empower us to ask good questions.” - Alberto Cairo, How Charts Lie
• Plots convey ideas (and beliefs)
• Scientific papers often structured (and read) by its figures
• Making plots is easy
• Conveying ideas is hard

1. It is truthful
2. It is functional
3. It is insightful
4. It is enlightening
5. It is beautiful

• Visualizations illustrate (from latin illustrare, to light up or illuminate)
• Leverage humans’ visual perception system
• This system is predictive/interpretive
  • i.e. it is a pattern recognition system
• When this system makes bad predictions, we can experience optical illusions

• pareidolia - “the tendency for perception to impose a meaningful interpretation on a nebulous stimulus, usually visual, so that one sees an object, pattern, or meaning where there is none”

1. We perceive value/hue of colors relative to adjacency colors
2. Certain geometry interferes with assessing true spatial relationships
3. We perceive area of shapes relative to adjacent shapes
4. We may perceive shapes where there are none
5. We may perceive shapes that look like other shapes

• Visualizations encode data values as visual properties
• An encoding is a mapping between a data range and a visual property
• Properties may include:
  • Length/width/height
  • Position
  • Area
  • Angle/proportional area
  • Shape
  • Color hue/value

• Every visualization uses one or more encodings
• Reading a plot requires decoding from visual back to numbers to form a mental model of the data
• Familiar encodings (e.g. position in a scatter plot) require less work to interpret than less conventional

data <- tibble(
  x=rnorm(100),
  y=rnorm(100,0,5)
)
data %>%
  ggplot(aes(x=x,y=y)) +
  geom_point()

data <- mutate(data,
  `x times y`=abs(x*y)
)
data %>%
  ggplot(aes(x=x,y=y,size=`x times y`)) +
  geom_point()

data <- mutate(data,
    z=runif(100),
    category=sample(c('A','B','C'), 100, replace=TRUE)
  )
data %>%
  ggplot(aes(x=x, y=y, size=`x times y`, color=z, shape=category)) +
  geom_point()

tibble(
  value=rnorm(100),
  category='A'
) %>%
  ggplot(aes(x=category,y=value,fill=category)) +
  geom_violin()

• Decoded visualizations represent relationships between data
• Different encodings enable more or less precise estimates of those relationships
• Translating from visualizations to quantiative estimates are perceptual tasks
• These tasks developed into a theory of elementary perceptual tasks by Cleveland and McGill

# two groups of samples with similar random data profiles
data <- as.matrix(
  tibble(
    A=c(rnorm(10),rnorm(10,2)),
    B=c(rnorm(10),rnorm(10,2)),
    C=c(rnorm(10),rnorm(10,2)),
    D=c(rnorm(10,4),rnorm(10,-1)),
    E=c(rnorm(10,4),rnorm(10,-1)),
    F=c(rnorm(10,4),rnorm(10,-1))
  )
)
rownames(data) <- paste0('G',seq(nrow(data)))
heatmap(data)

1. Visualize data in multiple ways
2. Perform statistical analyses to confirm patterns
3. Informative is better than beautiful
4. No plot is better than a useless plot
5. Sometimes a table is the best way to present data
6. If there is text on a plot, it should be legible
7. Almost every plot should have properly labeled axes
8. Be color-blind friendly
9. Make differences appear as big as they mean

library(patchwork)
data <- tibble(
  percent=c(86,88,87,90,93,89),
  ID=c('A','B','C','D','E','F')
)
g <- ggplot(data, aes(x=ID,y=percent)) +
  geom_bar(stat="identity")

g + coord_cartesian(ylim=c(85,95)) | g

## # A tibble: 20 × 8
##    ID    age_at_death condition    tau  abeta   iba1   gfap braak_stage
##    <chr>        <dbl> <fct>      <dbl>  <dbl>  <dbl>  <dbl> <fct>      
##  1 A1              73 AD         96548 176324 157501  78139 4          
##  2 A2              82 AD         95251      0 147637  79348 4          
##                              ...
## 10 A10             69 AD         48357  27260  47024  78507 2          
## 11 C1              80 Control    62684  93739 131595 124075 3          
## 12 C2              77 Control    63598  69838   7189  35597 3          
##                              ...
## 20 C10             73 Control    15781  16592  10271 100858 1

• Every plot is the combination of three types of information:
  1. data (i.e. values)
  2. geometry (i.e. shapes)
  3. aesthetics (i.e. connects values and shapes)

• Each layer is a set of data connected to a geometry and an aesthetic

• Each geom_X() function adds a layer to a plot

• The plot has three layers:

  ggplot(data=ad_metadata, mapping=aes(x=age_at_death)) +
    geom_point(mapping=aes(y=tau, color='blue')) +
    geom_point(mapping=aes(y=abeta, color='red')) +
    geom_point(mapping=aes(y=iba1, color='cyan'))

• A scale maps data onto a range, e.g.:
  • pixel range
  • color on a gradient/set of colors
  • shape type, circle or square
  • shape dimension, like circle radius
• Multiple layers on the same plot
  • Must share at least one scale to be plotted together
  • May differ in one or more scales to be distinguished from each other

• One dimensional data
  • Bar chart
  • Lollipop plots
  • Stacked Area charts
• Visualizing Distributions
  • Histogram
  • Density plots
  • Boxplots
  • Violin Plots
  • Beeswarm Plots
  • Ridgeline Plots

• Scatter plots visualize pairs of quantities, usually continuous, as points in a two dimensional space
• Usually in cartesian coordinates, but polar coordinates or other types of coordinate systems are possible

ggplot(ad_metadata,mapping=aes(x=abeta, y=tau)) +
  geom_point(size=3)

ggplot(ad_metadata,mapping=aes(x=abeta, y=tau)) +
  geom_point(size=3)

ggplot(ad_metadata,mapping=aes(x=abeta, y=tau, shape=condition)) +
  geom_point(size=3)

g <- ggplot()
for(x in 0:5) {
  for(y in 0:4) {
    if(x+y*6 < 26) {
      g <- g + geom_point(
        tibble(x=x,y=y),
        aes(x=x,y=y),
        shape=x+y*6,size=8) +
       geom_label(
         tibble(x=x,y=y,label=x+y*6),
         aes(x=x,y=y+0.5,label=label)
       )
    }
  }
}
g

• Controlling which shapes are mapped to which value can be accomplished with scale_shape_manual():

ggplot(ad_metadata,mapping=aes(x=abeta, y=tau, shape=condition)) +
  geom_point(size=3) +
  scale_shape_manual(values=c(3,9))

• Color encodings added using either continuous or discrete values:

library(patchwork)
g <- ggplot(ad_metadata)
g_condition <- g + geom_point(
  mapping=aes(x=abeta, y=tau, color=condition),
  size=3
)
g_age <- g + geom_point(
  mapping=aes(x=abeta, y=tau, color=age_at_death),
  size=3
)
g_condition / g_age

• Close relative of the scatter plot where the area of the point markers is proportional to a third dimension

ggplot(ad_metadata,mapping=aes(x=abeta, y=tau, size=age_at_death)) +
  geom_point(alpha=0.5)

• Close relative of the scatter plot where certain pairs of points are connected with a line

arrange(ad_metadata,age_at_death) %>%
  mutate(
    x=abeta,
    xend=lag(x,1),
    y=tau,
    yend=lag(y,1)
  ) %>%
  ggplot() +
  geom_segment(aes(x=abeta, xend=xend, y=tau, yend=yend)) +
  geom_point(aes(x=x,y=y,shape=condition,color=condition),size=3)

• Line plots connect pairs of points with a line without drawing a symbol at each point
• geom_line() function draws lines between pairs of points sorted by \(x\) axis by default

ggplot(ad_metadata,mapping=aes(x=abeta, y=tau)) +
    geom_line()

• Plot multiple lines using the group aesthetic mapping

pivot_longer(ad_metadata,
  c(tau,abeta,iba1,gfap),
  names_to='Marker',
  values_to='Intensity'
  ) %>%
  ggplot(ad_metadata,mapping=aes(x=ID, y=Intensity, group=Marker, color=Marker)) +
    geom_line()

• Plot multiple lines using the group aesthetic mapping

• Line plots where:
  • 2+ continuous variables given vertical position encodings and
  • Each sample has its own line
• Each vertical axis can have a different scale

library(GGally)

ggparcoord(ad_metadata,
           columns=c(2,4:8),
           groupColumn=3,
           showPoints=TRUE
           ) +
  scale_color_manual(values=c("#bbbbbb", "#666666"))

• Colors can be specified with a 6- or 8- hexit hexadecimal code
• Hexit - 0 - f, 0=0 and f=16
• Codes form a triplet #rrggbb
  • rr is the value of the color red
  • gg for green
  • bb for blue
• #ffffff is the color white
• #000000 is the color black
• #ff0000 is the color red
• #0000ff is the color blue
• #7fff00 is this color (called chartreuse)

• Heatmaps visualize values associated with a grid of points \((x,y,z)\) as a grid of colored rectangles
• \(x\) and \(y\) define the grid point coordinates and \(z\) is a continuous value
• A common heatmap you might have seen is the weather map, which plots current or predicted weather patterns on top of a geographic map:

• Heatmaps are often used to visualize matrices
• Can create heatmap in R using the base R heatmap() function:
• heatmap() function creates a clustered heatmap where the rows and columns have been hierarchically clustered

# heatmap() requires a R matrix, and cannot accept a tibble or a dataframe
marker_matrix <- as.matrix(
  dplyr::select(ad_metadata,c(tau,abeta,iba1,gfap))
)
# rownames of the matrix become y labels
rownames(marker_matrix) <- ad_metadata$ID

heatmap(marker_matrix)

• Performs hierarchical clustering of the rows and columns using a Euclidean distance function
• Draws dendrograms on the rows and columns
• Scales the data in the rows to have mean zero and standard deviation 1
• Can alter this behavior with arguments:

heatmap(
  marker_matrix,
  Rowv=NA, # don't cluster rows
  Colv=NA, # don't cluster columns
  scale="none", # don't scale rows
)

• The scale mapping \(z\) values to colors is very important when interpreting heatmaps
• heatmap() function has the major drawback that no color key is provided!
• heatmap.2() in gplots package has a similar interface
• Provides more parameters to control the behavior of the plot and includes a color key:

library(gplots)
heatmap.2(marker_matrix)

• heatmap() and heatmap.2() can annotate rows and columns with a categorical variable along the margins

# with heatmap()
condition_colors <-
  transmute(
    ad_metadata,
    color=if_else(condition == "AD","red","blue")
  )
heatmap(
  marker_matrix,
  RowSideColors=condition_colors$color
)

# with heatmap.2()
heatmap.2(
  marker_matrix,
  RowSideColors=condition_colors$color
)

• “Heatmaps” in ggplot use geom_tile geometry
• geom_tile requires data in long format with x, y, and z values

pivot_longer(
  ad_metadata,
  c(tau,abeta,iba1,gfap),
  names_to="Marker",
  values_to="Intensity"
) %>%
  ggplot(aes(x=Marker,y=ID,fill=Intensity)) +
  geom_tile()

• Heatmap color palette specified using native color palettes

• Heatmap color palette specified using native color palettes passed to col argument

# native R colors are:
# - rainbow(n, start=.7, end=.1)
# - heat.colors(n)
# - terrain.colors(n)
# - topo.colors(n)
# - cm.colors(n)
# the n argument specifies the number of colors
# (i.e. resolution) of the colormap to return
heatmap(marker_matrix,col=cm.colors(256))

heatmap(marker_matrix,col=cm.colors(256))

heatmap(marker_matrix,col=cm.colors(2))

• With ggplot and geom_tile(), use the scale_fill_gradientn function to specify a different color palette

pivot_longer(
  ad_metadata,
  c(tau,abeta,iba1,gfap),
  names_to="Marker",
  values_to="Intensity"
) %>%
  ggplot(aes(x=Marker,y=ID,fill=Intensity)) +
  geom_tile() +
  scale_fill_gradientn(colors=cm.colors(256))

• May use ColorBrewer palettes in the RColorBrewer package
• Sensible choices on color palettes, including colorblind-safe

• Heatmaps are quite complicated and can easily mislead us

• Four factors influence how a dataset can be visualized as a heatmap:

  1. The type of features, i.e. whether the features are continuous or discrete
  2. The relative scales of the features
  3. The total range of the data
  4. Whether or not the data are centered

• Continuous features map numeric values to a color gradient

• Generally, all features in heatmap must be on a comparable scale, or transformed appropriately to attain this

data <- tibble(
  ID=paste0('F',seq(10)),
  a=rnorm(10,0,1),
  b=rnorm(10,100,20),
  c=rnorm(10,20,5)
) %>%
  pivot_longer(c(a,b,c))

ggplot(data,aes(x=name,y=ID,fill=value)) +
  geom_tile()

library(ggbeeswarm)
ggplot(data) +
  geom_beeswarm(aes(x=name,y=value,color=name))

• Features with different ranges must be scaled so they are all comparable
• e.g. z-transform

data %>%
  pivot_wider(id_cols='ID',names_from=name) %>%
  mutate(
    across(c(a,b,c),scale)
  ) %>%
  pivot_longer(c(a,b,c)) %>%
  ggplot(aes(x=name,y=ID,fill=value)) +
  geom_tile()

• Scaling rows vs columns dramatically changes the heatmap

data %>%
  pivot_wider(id_cols=name,names_from=ID) %>%
  mutate(
    across(starts_with('F'),scale)
  ) %>%
  pivot_longer(starts_with('F'),names_to="ID") %>%
  ggplot(aes(x=name,y=ID,fill=value)) +
  geom_tile()

• Extreme values, i.e. outliers, in any of the features can render a heatmap uninformative

tibble(
  ID=paste0('F',seq(10)),
  a=rnorm(10,0,1),
  b=rnorm(10,0,1),
  c=c(rnorm(9,0,1),1e9)
) %>%
  pivot_longer(c(a,b,c)) %>%
  ggplot(aes(x=name,y=ID,fill=value)) +
  geom_tile()

• Heatmaps “work best” when data are normally distributed
• If they are not:

data <- tibble(
  ID=paste0('F',seq(10)),
  a=10**rnorm(10,4,1),
  b=10**rnorm(10,4,1),
  c=10**rnorm(10,4,1)
) %>%
  pivot_longer(c(a,b,c))
data %>%
  ggplot(aes(x=name,y=ID,fill=value)) +
  geom_tile()

• Some features have a meaningful “center”
  • e.g. log2 fold change of 0 divides data into up and down
• A diverging color palette appropriate in these cases
  
• Be sure to align the center of the color palette with center value
  • e.g. midpoint=0 when central value is 0

tibble(
  ID=paste0('F',seq(10)),
  a=rnorm(10,0,1),
  b=rnorm(10,0,1),
  c=rnorm(10,0,1)
) %>%
  pivot_longer(c(a,b,c)) %>%
  ggplot(aes(x=name,y=ID,fill=value)) +
  geom_tile() +
  scale_fill_gradient2(
    low="#000099", mid="#ffffff", high="#990000",
    midpoint=0
  )

• These data centered around 1, but default centers color palette around 0!

tibble(
  ID=paste0('F',seq(10)),
  a=rnorm(10,1,1),
  b=rnorm(10,1,1),
  c=rnorm(10,1,1)
) %>%
  pivot_longer(c(a,b,c)) %>%
  ggplot(aes(x=name,y=ID,fill=value)) +
  geom_tile() +
  scale_fill_gradient2(low="#000099", mid="#ffffff", high="#990000")

• Be sure to set midpoint appropriately!

• Whole genome data can produce long vectors of data
  • e.g. read pileup across all chromosomes
• Screens/publication formats have limited space
• How to visualize an entire genome in a rectangular space?
• How to depict relationships between disparate genomic loci?
• Circos is a software package originally designed to handle this kind of data

• Circos Genomics Data Example

• Circos is written in PERL
• circlize package provides R implementation

• Often want to put multiple plots in same figure
• Two approaches:
  • subplots: combine unrelated plots into one figure
  • facet wrapping: separate the same dataset into different plots

• patchwork library composes ggplot objects together using an intuitive set of operators:
  • a | b - put plots side-by-side
  • a / b - put plot a above b
  • (a | b) / c - put a and b side-by-side, and c below them

data <- tibble(
  a=rnorm(100,0,1),
  b=rnorm(100,3,2)
)
g_scatter <- ggplot(data, aes(x=a, y=b)) +
  geom_point()
g_violin <- pivot_longer(data, c(a,b)) %>%
  ggplot(aes(x=name,y=value,fill=name)) +
  geom_violin()

g_scatter | g_violin

g_scatter / g_violin

g_scatter / ( g_scatter | g_violin)

(g_scatter / g_scatter ) | g_violin

• Facet wrapping separates subsets of a dataset into plots with identical axes

library(mvtnorm) # package implementing multivariate normal distributions
nsamp <- 100
data <-  rbind(
    rmvnorm(nsamp,c(1,1),sigma=matrix(c(1,0.8,0.8,1),nrow=2)),
    rmvnorm(nsamp,c(1,1),sigma=matrix(c(1,-0.8,-0.8,1),nrow=2)),
    rmvnorm(nsamp,c(1,1),sigma=matrix(c(1,0,0,1),nrow=2))
)
colnames(data) <- c('x','y')
g_oneplot <- as_tibble(data) %>%
  mutate(
    sample_name=c(rep('A',nsamp),rep('B',nsamp),rep('C',nsamp))
  ) %>%
  ggplot(aes(x=x,y=y,color=sample_name)) +
  geom_point()
g_oneplot

• Plot may be split into three using the facet_wrap() function

g_oneplot + facet_wrap(vars(sample_name))

• Can apply transforms to each facet

g_oneplot + facet_wrap(vars(sample_name)) +
  geom_smooth(method="loess", formula=y ~ x)

• ggplot styling is plain and recognizeable
• Some journals may have strict formatting requirements
• Tweaking plot aesthetics in code can be very tedious
• Can address these issues with
  • ggplot themes
  • Exporting to Scalable Vector Graphics (SVG) format

• Themes in ggplot are combinations of styling elements applied to the different components of a chart

base_g <- tibble(
  x=rnorm(100),
  y=rnorm(100)
) %>%
  ggplot(aes(x=x, y=y)) +
  geom_point()

base_g

• ggplot comes with other themes that may be added to plots with theme_X() functions

base_g + theme_bw()

base_g + theme_classic()

• All ggplot plots may be saved in Scalable Vector Graphics (SVG) format
• SVG is an XML format describes shapes using a mathematical specification
• e.g. a circle:

<circle cx="50" cy="50" r="50"/>

• Illustration programs can edit the individual elements of the entire plot

• Save to SVG format by using ggsave() function

ggsave('multipanel.svg')

## Saving 7.5 x 4.5 in image