WeightedTreemaps

Michael Jahn, David Leslie, Ahmadou Dicko 2021-12-09

Generate and plot Voronoi treemaps or Sunburst treemaps from hierarchical data.

News

25 March 2021

A Shiny app for generating treemaps from custom data is now available on Shinyapps.io!

Description

Treemaps are a visually appealing graphical representation of numerical data using a space-filling approach. A plane or ‘map’ is subdivided into smaller areas called cells. The cells in the map are scaled according to an underlying metric which allows to grasp the hierarchical organization and relative importance of many objects at once. This package contains two different implementations of treemaps, Voronoi treemaps and Sunburst treemaps

There are different implementations available for Voronoi tesselations in R, the simplest being the deldir() function (from package deldir). However, deldir and others do not handle nested Voronoi tesselations, nor do they perform additively weighted Voronoi tesselation. This is an important demand for systems biology and other applications where it is useful to scale the cell size (or area) to a set of predefined weights. The voronoiTreemap() function provided in this packages allows both the additively weighted Voronoi tesselation and the nesting of different hierarchical levels in one plot.

Some of the underlying functions for the tesselation were developed by Paul Murrell, University of Auckland, and serve as the basis for this package. They are called by a recursive wrapper function, voronoiTreemap(), which subdivides the plot area in polygonal cells according to the highest hierarchical level. It then continues with the tesselation on the next lower level using the child cell of the previous level as the new parental cell, and so on.

The Sunburst treemap is a computationally less demanding treemap that does not require iterative refinement, but simply generates circle sectors that are sized according to predefined weights. The main function to draw Sunburst treemaps is sunburstTreemap(). It uses the same underlying recursive algorithm under the hood and can be used to draw sectors of different hierarchical levels with increasing granularity.

Requirements

The C++ code computing the actual Voronoi tesselation requires the CGAL library headers. Thanks to Ahmadou Dicko, installing the complete CGAL library locally is no longer necessary. Instead, the package depends on the CGAL4 headers that are now available on CRAN as R package cgal4h. The dependencies are installed automatically and manual installation of CGAL (headers) should not be necessary.

Installation

To install the package directly from github, use the following function from the devtools package in your R session:

devtools::install_github("m-jahn/WeightedTreemaps")

Usage

Voronoi treemaps

The functions to create Voronoi (or Sunburst) treemaps take a data.frame as main input. The data.frame should contain column(s) with numerical or categorical data (i.e. a character vector). Let’s create a simple example data frame.

library(WeightedTreemaps)

# load example data
data(mtcars)
mtcars$car_name = gsub(" ", "\n", row.names(mtcars))

Generate the treemap. It will return a list of polygons and metadata. The columns of the data frame that are used as levels of the treemap need to be specified. Different parameters like the initial shape, or the maximum number of iterations are optional.

# generate treemap; set seed to obtain same pattern every time
tm <- voronoiTreemap(
  data = mtcars,
  levels = c("gear", "car_name"),
  cell_size = "wt",
  shape = "rounded_rect",
  seed = 123
)

Draw the treemap.

drawTreemap(tm, label_size = 2.5, label_color = "white")

The voronoiTreemap() and drawTreemap() functions are separated in order to allow drawing of the same treemap object in different ways. Computation of treemaps with thousands of cells can be very time and resource consuming (around 5-10 minutes for a 2000-cell treemap on a regular desktop computer). With the drawTreemap() function, we can not only plot the same treemap in different ways but also combine several treemaps on one page using the layout and position arguments. The most important style element is color. Coloring can be based on cell category, cell size, or both, using the color_type argument. By default, the highest hierarchical level is used for coloring but that can be customized using the color_level argument.

drawTreemap(tm, title = "treemap 1", label_size = 2,
  color_type = "categorical", color_level = 1,
  layout = c(2, 2), position = c(1, 1), legend = TRUE)
#> Note: use 'add = TRUE' if you want to add more treemaps to this page.

drawTreemap(tm, title = "treemap 2", label_size = 2,
  color_type = "categorical", color_level = 2, border_size = 3,
  add = TRUE, layout = c(2, 2), position = c(1, 2), legend = TRUE)

drawTreemap(tm, title = "treemap 3", label_size = 2,
  color_type = "both", color_level = 1,
  add = TRUE, layout = c(2, 2), position = c(2, 1), legend = TRUE)

drawTreemap(tm, title = "treemap 4", label_size = 2,
  color_type = "cell_size", color_level = 2,
  color_palette = heat.colors(10),
  border_color = grey(0.4), label_color = grey(0.4),
  add = TRUE, layout = c(2, 2), position = c(2, 2),
  title_color = "black", legend = TRUE)

Positioning of cells

Generating a Voronoi treemap is an iterative and somewhat random process. Since the cells ‘move’ during the iteration process, it can be difficult to control the exact final position of cells. However, there are two ways to influence cell positioning. The first is to use different algorithms for sampling initial coordinates for each cell. The second is simply setting a seed, which will sample the same set of starting coordinates for the same input data. Regarding the positioning argument, compare the following three examples where initial positions are 1) random, 2) ordered from top to bottom, or 3) ordered from center to edges.

# set seed to obtain same df every time
set.seed(123)
df <- data.frame(A = sample(10:100, 45))

tm1 <- voronoiTreemap(
  data = df, levels = "A",
  cell_size = "A",
  shape = "rounded_rect",
  positioning = "random"
)

tm2 <- voronoiTreemap(
  data = df, levels = "A",
  cell_size = "A",
  shape = "rounded_rect",
  positioning = "regular"
)

tm3 <- voronoiTreemap(
  data = df, levels = "A",
  cell_size = "A",
  shape = "rounded_rect",
  positioning = "clustered"
)

drawTreemap(tm1, title = "positioning = 'random'", border_size = 3,
  layout = c(1,3), position = c(1, 1))
#> Note: use 'add = TRUE' if you want to add more treemaps to this page.

drawTreemap(tm2, title = "positioning = 'regular'", border_size = 3,
  add = TRUE, layout = c(1,3), position = c(1, 2))

drawTreemap(tm3, title = "positioning = 'clustered'", border_size = 3,
  add = TRUE, layout = c(1,3), position = c(1, 3))

Custom initial shapes

Instead of using predefined shapes, we can also supply a custom set of coordinates to plot a treemap using the `shape``argument. The validity of the supplied coordinates is not checked, so all responsibility lies with the user (!). The R session might even crash (due to C++ dependency) if a shape is supplied that is too irregular or edgy, and the tesselation becomes unfeasible. Here are some stable examples.

# different initial shapes, the more squared the better
house_coords <- list(
  x = c(0, 10, 10, 5, 0),
  y = c(0, 0, 10,15,10))

rect_coords <- list(
  x = c(0, 10, 10, 0),
  y = c(0, 0, 3, 3))

oct_coord <- list(
  x = sin(seq(0, 2, 2/8)*pi) * 1000 + 1000,
  y = cos(seq(0, 2, 2/8)*pi) * 1000 + 1000
)

Let’s generate treemaps with the shapes of a house, a rectangle, or an octogon.

tm1 <- voronoiTreemap(data = df, levels = "A",
  shape = house_coords)

tm2 <- voronoiTreemap(data = df, levels = "A",
  shape = rect_coords)

tm3 <- voronoiTreemap(data = df, levels = "A",
  shape = oct_coord)

drawTreemap(tm1, layout = c(1,3), position = c(1, 1))
#> Note: use 'add = TRUE' if you want to add more treemaps to this page.
drawTreemap(tm2, add = TRUE, layout = c(1,3), position = c(1, 2))
drawTreemap(tm3, add = TRUE, layout = c(1,3), position = c(1, 3))

Advanced example for Voronoi treemaps

This example will cover the generation of a somewhat larger treemap, as it is often useful to visualize e.g. many genes or proteins at once in molecular biology studies. However, treemaps can be used for any type of data visualization. First we read a proteomics test data set from Jahn et al., Cell Reports, 2018. (https://www.cell.com/cell-reports/fulltext/S2211-1247(18)31485-2) This dataset contains thousands of protein measurements of the cyanobacterium Synechocystis sp. PCC6803.

# additional libraries for data filtering and colors
library(dplyr)
library(colorspace)

# pick the top most abundant proteins
df <- Jahn_CellReports_2018 %>%
  filter(condition == "CO2-0-15") %>%
  arrange(desc(mean_mass_fraction_norm)) %>%
  slice(1:1000)

We can generate the Voronoi treemap using some more of the function’s parameters. We can increase maxIterations and decrease error_tol which will lead to lower errors (difference between target cell size and actual cell size). Set a seed to obtain a similar arrangement of cells for similar maps, otherwise starting positions will be sampled more randomly. The positioning argument clustered_by_area will try to place cells with bigger target area in the middle and smaller area at the edges.

tm <- voronoiTreemap(
  data = df,
  levels = c("Process.abbr", "protein"),
  cell_size = "mean_mass_fraction_norm",
  shape = "rectangle",
  error_tol = 0.005,
  maxIteration = 200,
  positioning = "clustered_by_area",
  seed = 1
)

Generating and plotting of treemaps are two processes separated on purpose. Computing treemaps can be time-consuming and to recalculate them every time just for changing a color gradient or label size is inefficient. Once a treemap is computed, it can be drawn in different ways as the following example shows. First we can generate custom color palettes using colorspaces hclwizard. Just browse to the Export and then the R tab and copy the code to your script.

# outcomment to run interactive wizard:
#hclwizard()

custom_pal_1 <- sequential_hcl(
  n = 20,
  h = c(-46, 78),
  c = c(61, 78, 54),
  l = c(60, 91),
  power = c(0.8, 1),
  rev = TRUE
)

custom_pal_2 <- diverging_hcl(
  n = 7, 
  h = c(340, 128), 
  c = c(60, 80), 
  l = c(75, 97), 
  power = c(0.8, 1.5),
  rev = TRUE
)

Draw a customized treemap using some of the graphical parameters. Compare two different color palettes.

drawTreemap(
  tm, 
  color_palette = custom_pal_1,
  color_type = "cell_size",
  color_level = 2,
  label_level = c(1,2),
  label_size = 2,
  label_color = grey(0.5),
  border_color = grey(0.65),
  layout = c(1, 2),
  position = c(1, 1)
)

drawTreemap(
  tm, 
  color_palette = custom_pal_2,
  color_type = "cell_size",
  color_level = 2,
  label_level = c(1,2),
  label_size = 2,
  label_color = grey(0.5),
  border_color = grey(0.9),
  layout = c(1, 2),
  position = c(1, 2),
  add = TRUE
)

Generate treemaps with parallel computing

This is an example how several treemaps can be computed in parallel. This functionality is not part of this package but just makes use of functions contained in the parallel package. First read the test data set with cyanobacterial proteomics data from 10 different growth conditions. Only the most abundant proteins are selected for treemap generation to reduce computation time.

library(parallel)

df <- Jahn_CellReports_2018 %>%
  group_by(condition) %>%
  arrange(desc(mean_mass_fraction_norm)) %>%
  slice(1:200)

Generate 10 treemaps using the parallel version of lapply, and the condition annotation to subset the data frame. Note that you can adjust the mc.cores parameter to the number of CPUs available on your computer. The positioning parameter can also take a vector of length(levels) to make cell positions on the first level more comparable between different treemaps.

tm <- mclapply(
  unique(df$condition), 
  mc.cores = 10, 
  mc.set.seed = FALSE,
  FUN = function(cond) {
    
    voronoiTreemap(
      data = filter(df, condition == cond),
      levels = c("Process.abbr", "protein"), 
      cell_size = "mean_mass_fraction_norm",
      custom_color = "mean_mass_fraction_norm",
      shape = "rounded_rect",
      positioning = c("regular", "clustered_by_area"),
      maxIteration = 50,
      error_tol = 0.01
    )
  }
)

Draw all 10 treemaps on one canvas using layout and position arguments.

lapply(1:10, function(i) {
  
  drawTreemap(
    tm[[i]],
    color_type = "custom_color",
    color_level = 2,
    color_palette = custom_pal_2,
    custom_range = c(0, 0.05),
    border_size = 6,
    border_color = grey(0.9),
    label_level = c(1,2),
    label_size = 1.5,
    label_color = grey(0.4),
    legend = TRUE,
    title = unique(df$condition)[i],
    title_size = 1.5,
    title_color = grey(0.4),
    layout = c(2, 5),
    position = c(
      ifelse(i <= 5, 1, 2),
      ifelse(i <= 5, i, i-5)),
    add = ifelse(i == 1, FALSE, TRUE)
  )
  
}) %>% invisible

Sunburst treemaps

Sunburst treemaps are generated in the same way as described above for Voronoi treemaps. The function to generate a sunburst treemap is sunburstTreemap(), and just like voronoiTreemap() it returns an object of class treemapResult (essentially a list) with polygons and metadata. Drawing is done using the same drawTreemaps() function as for Voronoi treemaps.

# generate data frame
set.seed(123)
df <- data.frame(
  A = rep(c("a", "b", "c"), each = 15),
  B = sample(letters[4:12], 45, replace = TRUE)
)

head(df)
#>   A B
#> 1 a f
#> 2 a f
#> 3 a e
#> 4 a i
#> 5 a h
#> 6 a g

Generate sunburst treemap.

# by default cell (sector) size is encoded by number of members per group
tm <- sunburstTreemap(
  data = df,
  levels = c("A", "B")
)

Draw treemaps with different graphical parameters

# draw treemap with default options
drawTreemap(tm,
  title = "A sunburst treemap",
  legend = TRUE,
  border_size = 2,
  label_color = grey(0.6),
  layout = c(1, 3),
  position = c(1, 1)
)
#> Note: use 'add = TRUE' if you want to add more treemaps to this page.

# use custom color palette
drawTreemap(tm,
  title = "Use custom palette",
  legend = TRUE,
  color_palette = rep(c("#81E06E", "#E68CFF", "#76BBF7"), c(3, 4, 5)),
  border_size = 2,
  label_level = 2,
  label_size = 0.7,
  label_color = grey(0.5),
  layout = c(1, 3),
  position = c(1, 2),
  add = TRUE
)

# color cells (sectors) based on cell size
drawTreemap(tm,
  title = "Coloring encoded by cell size",
  color_type = "cell_size",
  legend = TRUE,
  color_palette = rev(heat.colors(10)),
  border_size = 3,
  border_color = grey(0.3),
  label_level = 1,
  label_size = 2,
  label_color = grey(0.3),
  layout = c(1, 3),
  position = c(1, 3),
  add = TRUE
)

References and other treemap packages

The Voronoi tesselation is based on functions from Paul Murrell, https://www.stat.auckland.ac.nz/~paul/Reports/VoronoiTreemap/voronoiTreeMap.html. We created a recursive wrapper around the main tesselation function and improved the stability regarding generation of larger treemaps.

For a similar but JAVA based implementation of Voronoi treemaps wrapped in R, see David Leslie’s scripts at https://github.com/dlesl/voronoi_treemap_rJava.

A Javascript based R package lets you draw simple treemaps in your browser, however, this is not suitable for treemaps with many (as, hundreds of) cells. The package is available from CRAN or github, https://github.com/uRosConf/voronoiTreemap.

Another popular resource is the web-based treemap generation from University of Greifswald at https://bionic-vis.biologie.uni-greifswald.de/.

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