• 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

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()

data <-  mutate(data, `x + y`=x+y) %>%
  arrange(`x + y`) %>%
  mutate(
    xend=lag(x,1),
    yend=lag(y,1)
  )
data %>%
  ggplot() +
  geom_segment(aes(x=x,xend=xend,y=y,yend=yend,alpha=0.5)) +
  geom_point(aes(x=x, y=y, size=`x times y`, color=z, shape=category))

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

• 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)

• A simple example dataset:

  ## # 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

• Goal: visualize the relationship between age at death and the amount of tau pathology
• Try a scatter plot where each marker is a subject with
  • \(x\) is age_at_death
  • \(y\) is tau

  ggplot(
      data=ad_metadata,
      mapping = aes(
        x = age_at_death,
        y = tau
      )
    ) +
    geom_point()

ggplot(data=ad_metadata, mapping=aes(x=age_at_death, y=tau)) +
  geom_point()

ggplot(data=ad_metadata, mapping=aes(x=age_at_death, y=tau)) +
  geom_point()

1. ggplot() - function creates a plot
2. data= - pass a tibble with the data
3. mapping=aes(...) - Define an aesthetics mapping connecting data to plot properties
4. geom_point(...) - Specify geometry as points where marks will be made at pairs of x,y coordinates

Is this the whole story?

• There are both AD and Control subjects in this dataset!

• How does condition relate to this relationship we see?

• Layer on an additional aesthetic of color:

  ggplot(
      data=ad_metadata,
      mapping = aes(
        x = age_at_death,
        y = tau,
        color=condition # color each point
      )
    ) +
    geom_point()

ggplot(data=ad_metadata, mapping=aes(
      x=age_at_death, y=tau, color=condition
    )) + geom_point()

• Differences in distributions of variables can be important

• Examine the distribution of age_at_death for AD and Control samples with violin geometry with geom_violin():

  ggplot(data=ad_metadata, mapping = aes(x=condition, y=age_at_death)) +
    geom_violin()

ggplot(data=ad_metadata, mapping = aes(x=condition, y=age_at_death)) +
  geom_violin()

• Can put multiple plots in one figure with patchwork library:

library(patchwork)
age_boxplot <- ggplot(
    data=ad_metadata,
    mapping = aes(x=condition, y=age_at_death)
  ) +
  geom_boxplot()
tau_boxplot <- ggplot(
    data=ad_metadata,
    mapping=aes(x=condition, y=tau)
  ) +
  geom_boxplot()

age_boxplot | tau_boxplot # this puts the plots side by side

age_boxplot | tau_boxplot # this puts the plots side by side

• Useful collection of plot types and examples:
• R Graph Gallery

• ggplot has two key concepts that give it great flexibility: layers and scales
• A layer is one set of data drawn with a geometry and an aesthetic
• A scale is the mapping from the data values to visual properties
• A plot may have one or more layers
• Different layers may share scales or have their own

• 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

How many layers? How many scales?

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

• Map length (i.e. height or width of rectangle) proportional to scalar value

ggplot(ad_metadata,
  mapping = aes(
    x=ID,
    y=tau)
  ) +
  geom_bar(stat="identity")

ggplot(ad_metadata, mapping = aes(x=ID,y=tau)) +
  geom_bar(stat="identity")

• Change the fill color of the bars based on condition:

ggplot(ad_metadata, mapping = aes(x=ID,y=tau,fill=condition)) +
  geom_bar(stat="identity")

ggplot(ad_metadata, mapping = aes(x=ID,y=tau,fill=condition)) +
  geom_bar(stat="identity")

• Bar charts can also plot negative numbers

mutate(ad_metadata, tau_centered=(tau - mean(tau))) %>%
  ggplot(mapping = aes(x=ID, y=tau_centered, fill=condition)) +
  geom_bar(stat="identity")

• Similar to bar charts, “lollipop plots” replace bar with a line segment and a circle
• No dedicated geometry - use geom_point and geom_segment layers:

ggplot(ad_metadata) +
  geom_point(mapping=aes(x=ID, y=tau)) +
  geom_segment(mapping=aes(x=ID, xend=ID, y=0, yend=tau))

• Visualize multiple 1D data that share a common categorical axis

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

Stacked area plots require three pieces of data:

• x - a numeric or categorical axis for vertical alignment
• y - a numeric axis to draw vertical proportions
• group - a categorical variable that indicates which (x,y) pairs correspond to the same line

• Can view the relative proportion of values in each category rather than the actual values

pivot_longer(
    ad_metadata,
    c(tau,abeta,iba1,gfap),
    names_to='Marker',
    values_to='Intensity'
  ) %>%
  group_by(ID) %>% # divide each intensity values by sum markers
  mutate(
    `Relative Intensity`=Intensity/sum(Intensity)
  ) %>%
  ungroup() %>% # ungroup restores the tibble to original number of rows
  ggplot(aes(x=ID,y=`Relative Intensity`,group=Marker,fill=Marker)) +
    geom_area()

• A distribution describes the general “shape” of a set of numbers
  • i.e. what is the relative frequency of the values, or ranges of values
• Must understand distribution of data to choose statistical methods appropriately

• First described by Karl Pearson
• Type of bar chart
• Divides up the range of a dataset from minimum to maximum into bins usually of the same size
• Each bin represented by a bar with height or width proportional to number of values that fall within that bin

ggplot(ad_metadata) +
  geom_histogram(mapping=aes(x=age_at_death))

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

ggplot(ad_metadata) +
  geom_histogram(mapping=aes(x=age_at_death),bins=10)

• Histogram of synthetic dataset of 1000 normally distributed values:

tibble(x=rnorm(1000)) %>%
  ggplot() +
  geom_histogram(aes(x=x))

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

• Can add multiple histograms to same plot

tibble(
  x=c(rnorm(1000),rnorm(1000,mean=4)),
  type=c(rep('A',1000),rep('B',1000))
) %>%
  ggplot(aes(x=x,fill=type)) +
  geom_histogram(bins=30, alpha=0.6, position="identity")

• Similar to histogram, except instead of binning the values draws a smoothly interpolated line that approximates the distribution

• Density plot is always normalized so the integral under the curve is approximately 1

  ggplot(ad_metadata) +
    geom_density(mapping=aes(x=age_at_death),fill="#c9a13daa")

library(patchwork)
hist_g <- ggplot(ad_metadata) +
  geom_histogram(mapping=aes(x=age_at_death),bins=30)
density_g <- ggplot(ad_metadata) +
  geom_density(mapping=aes(x=age_at_death),fill="#c9a13daa")

hist_g | density_g

library(patchwork)
normal_samples <- tibble(
  x=c(rnorm(1000),rnorm(1000,mean=4)),
  type=c(rep('A',1000),rep('B',1000))
)
hist_g <- ggplot(normal_samples) +
  geom_histogram(
    mapping=aes(x=x,fill=type),
    alpha=0.6, position="identity", bins=30
)
density_g <- ggplot(normal_samples) +
  geom_density(
    mapping=aes(x=x,fill=type),
    alpha=0.6, position="identity"
  )

hist_g | density_g

• The histogram depicts distribution as a “box and whiskers”
• Assume data are unimodal (i.e. roughly bell-shaped)
• Explicitly draws:
  • Median
  • 25th and 75th percentile (a.k.a. 1st and 3rd quartile)
  • “whiskers” that show further extents
  • Some have markers for outlier samples

ggplot(ad_metadata) +
  geom_boxplot(mapping=aes(x=condition,y=age_at_death))

ggplot(ad_metadata) +
  geom_boxplot(mapping=aes(x=condition,y=age_at_death))

normal_samples <- tibble(
  x=c(rnorm(1000),rnorm(1000,4),rnorm(1000,2,3)),
  type=c(rep('A',2000),rep('B',1000))
)
ggplot(normal_samples, aes(x=x,fill=type,alpha=0.6)) +
  geom_density()

ggplot(normal_samples, aes(x=type,y=x,fill=type)) +
  geom_boxplot()

library(patchwork)
g <- ggplot(normal_samples, aes(x=type,y=x,fill=type))
boxplot_g <- g + geom_boxplot()
violin_g <- g + geom_violin()

boxplot_g | violin_g

• Boxplots can be misleading

• violin plot produces a shape where the width is proportional to the density of values value along the x or y axis *Similar in principle to a histogram or a density plot

ggplot(ad_metadata) +
  geom_violin(aes(x=condition,y=tau,fill=condition))

• beeswarm plot similar to a violin plot
• Plots the data itself as points like in a scatter plot
• Points are ‘jittered’ so they don’t overlap

library(ggbeeswarm)
ggplot(ad_metadata) +
  geom_beeswarm(
    aes(x=condition,y=age_at_death,color=condition),
    cex=2,
    size=2
  )

• Typically only useful when the number of values is not too many or too few:

normal_samples <- tibble(
  x=c(rnorm(1000),rnorm(1000,4),rnorm(1000,2,3)),
  type=c(rep('A',2000),rep('B',1000))
)
ggplot(normal_samples, aes(x=type,y=x,color=type)) +
  geom_beeswarm()

ggplot(normal_samples, aes(x=type,y=x,color=type)) +
  geom_beeswarm()

• Can color bees by another value

normal_samples <- tibble(
  x=c(rnorm(100),rnorm(100,4),rnorm(100,2,3)),
  type=c(rep('A',200),rep('B',100)),
  category=sample(c('healthy','disease'),300,replace=TRUE)
)
ggplot(normal_samples, aes(x=type,y=x,color=category)) +
  geom_beeswarm()

• ridgeline charts plot many non-trivial distributions
• Simply multiple density plots drawn for different variables within the same plot

library(ggridges)

tibble(
  x=c(rnorm(100),rnorm(100,4),rnorm(100,2,3)),
  type=c(rep('A',200),rep('B',100)),
) %>%
  ggplot(aes(y=type,x=x,fill=type)) +
  geom_density_ridges()

## Picking joint bandwidth of 0.822

tibble(
  x=rnorm(10000,mean=runif(10,1,10),sd=runif(2,1,4)),
  type=rep(c("A","B","C","D","E","F","G","H","I","J"),1000)
) %>%
  ggplot(aes(y=type,x=x,fill=type)) +
  geom_density_ridges(alpha=0.6,position="identity")

## Picking joint bandwidth of 0.494

• 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)

# 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))

• 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

(g1 / g2) | g3

• Save to SVG format by using ggsave() function

ggsave('multipanel.svg')

## Saving 7.5 x 4.5 in image