Heatmaps with Package Seriation

Introduction

A Heatmap uses colored tiles to represent the values in a data matrix. Patterns can be easily seen if the rows and columns are appropriately reordered. There are many ways to reorder a matrix, and the order has a significant impact on the visualization’s usefulness. The package seriation implements a large number of reordering methods (see: the list with all implemented seriation methods). seriation also provides a set of functions to display reordered heatmaps:

How to cite the seriation package:

Hahsler M, Hornik K, Buchta C (2008). “Getting things in order: An introduction to the R package seriation.” Journal of Statistical Software, 25(3), 1-34. ISSN 1548-7660, doi:10.18637/jss.v025.i03 https://doi.org/10.18637/jss.v025.i03.

Prepare the data

As an example, we use the Wood dataset with the normalized gene expression data (a sample of 136 genes) for wood formation in poplar trees in 6 locations. In case the data already has some order, we randomly reorder rows and columns for this example.

library("seriation")
data("Wood")
Wood <- Wood[sample(nrow(Wood)), sample(ncol(Wood))]
dim(Wood)

## [1] 136   6

DT::datatable(round(Wood, 2))

Here is a simple heatmap without reordering. No structure is visible.

pimage(Wood)

Reordering in seriation

Many seriation methods are available. The manual page for seriate() describes the methods available in package seriation.

Methods of interest for heatmaps are dendrogram leaf order-based methods applied to rows and columns. This is done using method = "heatmap". The actual seriation method can be passed on as parameter seriation_method, but it has a suitable default if it is omitted. Here is an example:

o <- seriate(Wood, method = "Heatmap", seriation_method = "HC_Mean")
o

## object of class 'ser_permutation', 'list'
## contains permutation vectors for 2-mode data
## 
##   vector length seriation method
## 1           136          Heatmap
## 2             6          Heatmap

This is the order for rows and columns. The method heatmap automatically performs hierarchical clustering and then applies the seriation method for reordering of dendrogram leaves. Here we use the row/column mean to reorder the dendrogram. The resulting order (2 means second dimension, i.e., columns) can be shown, and the reordered dendrogram and a reordered image can be plotted.

get_order(o, 2)

## B A P E C D 
## 2 3 5 4 1 6

plot(o[[2]])
pimage(Wood, order = o)

Built-in heatmap function

Package seriation has several functions to display heatmaps.

Without dendrograms: pimage

The permutation image plot in seriation provides a simple heatmap. The order argument not only accepts a seriation order, but also a seriation method.

pimage(Wood, order = "Heatmap", seriation_method = "HC_complete", 
       main = "Wood (hierarchical clustering)")
pimage(Wood, order = "Heatmap", seriation_method = "HC_Mean", 
       main = "Wood (reorder by row/col mean)")
pimage(Wood, order = "Heatmap", seriation_method = "GW_complete", 
       main = "Wood (reorder by Gruvaeus and Wainer heuristic)")

## Registered S3 method overwritten by 'gclus':
##   method         from     
##   reorder.hclust seriation

pimage(Wood, order = "Heatmap", 
       main = "Wood (default - optimal leaf ordering)")

With dendrograms: hmap

Here are some typical reordering schemes.

hmap(Wood, method = "HC_complete", main = "Wood (hierarchical clustering)")
hmap(Wood, method = "HC_Mean", main = "Wood (reorder by row/col mean)")
hmap(Wood, method = "GW_complete", main = "Wood (reorder by Gruvaeus and Wainer heuristic)")
hmap(Wood, method = "OLO_complete", main = "Wood (opt. leaf ordering)")

Different linkage types can be added in the method name.

Package DendSer offers more dendrogram seriation methods. These methods can be registered using `register_DendSer()``

register_DendSer()

## Registering new seriation method 'DendSer' for 'dist' requested by register_DendSer()

## Registering new seriation method 'DendSer_BAR' for 'dist' requested by register_DendSer()

## Registering new seriation method 'DendSer_PL' for 'dist' requested by register_DendSer()

## Registering new seriation method 'DendSer_LPL' for 'dist' requested by register_DendSer()

## Registering new seriation method 'DendSer_ARc' for 'dist' requested by register_DendSer()

## Registering new seriation criterion 'ARc' for 'dist' using register_DendSer()

hmap(Wood, method = "DendSer_BAR", main = "Wood (banded anti-Robinson)")

With distance matrices instead of dendrograms: hmap

Instead of dendrograms, also reordered distance matrices can be displayed. Dark block around the diagonal indicate the cluster structure.

hmap(Wood, method = "HC_complete", 
     plot_margins = "distances",
     main = "Wood (hierarchical clustering)")

Also non-dendrogram-based reordering methods can be used. These methods reorder rows and columns. Instead of the dendrograms, reordered distance matrices are shown.

hmap(Wood, method = "MDS", main = "Wood (MDS)")
hmap(Wood, method = "MDS_angle", main = "Wood (Angle in 2D MDS space)")
hmap(Wood, method = "R2E", main = "Wood (Rank 2 ellipse seriation)")
hmap(Wood, method = "TSP", main = "Wood (Traveling salesperson)")

colors with pimage and hmap

hmap(Wood, col = grays())
hmap(Wood, col = greenred())

hmap(Wood, col = colorRampPalette(c("brown", "orange", "red"))( 100 ) )

hmap(Wood, col = viridis::viridis(100))

There are many other packages to create color palettes in R like RColorBrewer or colorspaces.

ggplot2

All options are also available for ggplot2 using gghmap(). Currently there is no support to display dendrograms.

if (!require("ggplot2")) install.packages("ggplot2")

## Loading required package: ggplot2

library(ggplot2)
gghmap(Wood, method = "OLO")

Using seriation with other packages

The package seriation can be used to compute reordering for other heatmap packages.

heatmap in package stats

This is R’s standard heatmap function. seriate() can be used to supply the reordered dendrogram.

o <- seriate(Wood, method = "Heatmap", seriation_method = "OLO")
heatmap(Wood, Rowv = as.dendrogram(o[[1]]), Colv = as.dendrogram(o[[2]]))

We can also supply the rank order for any seriation method as weights and the dendrogram will be reordered as close as possible to the seriation order.

o <- seriate(Wood, method = "Heatmap", seriation_method = "Spectral")
heatmap(Wood, Rowv =  get_rank(o, 1), Colv =  get_rank(o, 2))

Package heatmaply

The package creates interactive heatmaps. It already uses the package seriation for parameter seriate and supports the OLO and GW methods.

if (!suppressMessages(require("heatmaply"))) install.packages("heatmaply")

library("heatmaply")
heatmaply(Wood, seriate = "none", main = "HC")

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## ℹ The deprecated feature was likely used in the dendextend package.
##   Please report the issue at <https://github.com/talgalili/dendextend/issues>.
## This warning is displayed once per session.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

heatmaply(Wood, seriate = "OLO", main = "OLO")

Any dendrogram-based seriation method from seriation can be supplied.

o <- seriate(Wood, method = "Heatmap", seriation_method = "OLO_ward")
heatmaply(Wood, Rowv = o[[1]], Colv = o[[2]], main = "OLO (Ward)")

o <- seriate(Wood, method = "Heatmap", seriation_method = "Spectral")
heatmaply(Wood, Rowv = get_rank(o, 1), Colv = get_rank(o, 2), main = "Spectral")

Michael Hahsler