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Introduction

This workflow is about how to programmatically reorder rows & columns of a heatmap. Heatmap is a versatile visualization method for many data types. However, for heatmaps to be effective, we should consider reordering rows & columns. See this figure for an example.

Required Packages

library(tidyverse) 
library(patchwork) # not actually required, loaded for this tutorial only 

library(RColorBrewer)

Data

We will use this example data from my own research. This is a collaboration between Buell lab at UGA & O'Connor lab at the Max Planck Institute.

Don't worry about what this table is about, but this workflow should work with any kind of data. This is a tidyverse workflow, so the input data do need to be in the tidy format. See this tutorial for more info on tidy data.

my_data <- read_csv("../Data/heatmap_example.csv", col_types = cols())

head(my_data)

row and col will be the rows and columns of the heatmap. The value column will be used to color the heatmap.

Without reordering

Let's see what will happen if we don't reorder the rows and columns.

no_reorder <- my_data %>% 
  ggplot(aes(x = col, y = row)) +
  geom_tile(aes(fill = value)) +
  scale_fill_gradientn(colors = brewer.pal(9, "YlGnBu")) +
  theme_classic() +
  theme(axis.text.y.left = element_blank(),
        axis.ticks.y.left = element_blank())

no_reorder

ggsave("../Results/Heatmap_no_reorder.svg", height = 3.5, width = 4.2, bg = "white")
ggsave("../Results/Heatmap_no_reorder.png", height = 3.5, width = 4.2, bg = "white")

heatmap_no_reorder

As you can see, there is no pattern to be discerned here.

Reorder one dimension first

To make it easier to discern information hidden in the heatmap, we need to reorder rows & columns. My approach is reordering one of dimensions (rows or columns) first. Often we can reorder one dimension based on some practical meaning. For example, is one of the dimensions time series? Developmental stages? Different experimental conditions/treatments?

An example data where columns have practical meaning.

Let's say we have an experiment with 10 genes and 6 samples.

my_data2 <- expand.grid(
  genes = letters[1:10],
  samples = 1:6)

And let's say samples 1, 3, 5 are controls, and samples 2, 4, 6 are treatments. And let's say we want to reorder it such that the controls appear first in (left) in the heatmap.

my_data2 <- my_data2 %>% 
  mutate(samples = factor(samples, 
                          levels = c(1, 3, 5, 2, 4, 6))) 

head(my_data2)

To (re)order a column of the data frame, you can use factor(). Within the factor() function, you type in the desired order in levels = c(...).

Now, when you go plot it, what will we see?

my_data2 %>% 
  ggplot(aes(x = samples, y = genes)) +
  theme_classic()

ggsave("../Results/Reorder_1_dim.svg", height = 3, width = 3, bg = "white")
ggsave("../Results/Reorder_1_dim.png", height = 3, width = 3, bg = "white")

Reorder_one_dimension

Now you can see that the x axis is in this order 1, 3, 5, 2, 4, 6, which is the order we specified.

Programmatic reordering of rows and columns

What if we don't want to manually punch in the order? We can reorder them using same basic statistics: peak value and number of peak values.

  • peak value: at which column does a given row reaches its maximum value?
  • number of peak values: for any given column, how many rows reach their maximum values?

A really simple but effective way to order rows and columns is to reorder columns by number of peak values. After that, reorder rows by peak values.

  1. Columns that have most rows reaching peak values appear first (to the left of heatmap).
  2. Columns that have the least rows reaching peak values appear last (to the right of the heatmap).
  3. Rows that reach peak value for the 1st column appear on top.
  4. Rows that reach peak value for the last column appear on the bottom.

It might be easier to understand how this plays out with an actual heatmap.

Finding peak values and number of peak values

Let's come back to our my_data example. To find the peak value for each row, use group_by(row) followed by slice_max()

my_data_peak_values <- my_data %>% 
  group_by(row) %>% 
  slice_max(order_by = value, n = 1, with_ties = F) %>% 
  rename(peaked_at = col) %>% 
  select(-value)

head(my_data_peak_values)

Now we have a data frame, each row is a row that will appear in the heatmap. For each row, there is information on which column of the heatmap it peaks at.

To find how many rows peak at each column, use group_by(column) followed by count().

number_of_peaks <- my_data_peak_values %>% 
  group_by(peaked_at) %>% 
  count() %>% 
  arrange(-n)

head(number_of_peaks)

Now we have a data frame where each row is a column that will appear in the heatmap. And we have information on how many rows peaked at that column.

Now we will reorder rows by columns.

my_data_peak_values_reordered <- my_data_peak_values %>% 
  inner_join(number_of_peaks, by = "peaked_at") %>% 
  arrange(-n)  

my_data_peak_values_reordered

After finding these basic statistics, we can join these statistics to our main data frame.

my_data_reordered <- my_data %>% 
  inner_join(number_of_peaks, by = c("col" = "peaked_at")) %>% 
  mutate(col = reorder(col, -n)) %>%  # this reorders the columns
  select(-n) %>% 
  inner_join(my_data_peak_values_reordered, by = "row") %>% 
  mutate(peaked_at = reorder(peaked_at, n)) %>% 
  mutate(order_rows = as.numeric(peaked_at)) %>% 
  mutate(row = reorder(row, order_rows)) # this reorders the rows by the "peaked_at" column. 
  

head(my_data_reordered)

Now we can plot it

reordered_heatmap <- my_data_reordered %>% 
  ggplot(aes(x = col, y = row)) +
  geom_tile(aes(fill = value)) +
  scale_fill_gradientn(colors = brewer.pal(9, "YlGnBu")) +
  theme_classic() +
  theme(axis.text.y.left = element_blank(),
        axis.ticks.y.left = element_blank())

reordered_heatmap

... and do a side-by-side comparison.

wrap_plots(no_reorder+ 
             labs(title = "Not reordered"), 
           reordered_heatmap +
             labs(title = "Rows/columns reordered"),
           guides = "collect") 

ggsave("../Results/Heatmap_reorder.svg", height = 3.5, width = 8, bg = "white")
ggsave("../Results/Heatmap_reorder.png", height = 3.5, width = 8, bg = "white")

Side_by_side

Now we can see that a clear pattern emerged. Each column has a group of rows that reach peak level. Overall, the heatmap is also much easier to understand and is more informative.