Hands-on Exercise 9 Part III - Heatmap for Visualising and Analysing Multivariate Data
Author
Ke Ke
Published
June 11, 2024
Modified
June 27, 2024
Learning Objectives:
plot static and interactive heatmap for visualising and analysing multivariate data
Getting Started
Heatmaps visualise data through variations in colouring. When applied to a tabular format, heatmaps are useful for cross-examining multivariate data, through placing variables in the columns and observation (or records) in rowa and colouring the cells within the table. Heatmaps are good for showing variance across multiple variables, revealing any patterns, displaying whether any variables are similar to each other, and for detecting if any correlations exist in-between them.
Installing and loading the required libraries
The following R packages will be used:
seriation
heatmaply
dendextend
tidyverse
Code chunk below will be used to check if these packages have been installed and also will load them into the working R environment.
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The downloaded binary packages are in
C:\Users\idrin\AppData\Local\Temp\RtmpOwg9eB\downloaded_packages
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The downloaded binary packages are in
C:\Users\idrin\AppData\Local\Temp\RtmpOwg9eB\downloaded_packages
Importing Data into R
The Data
The data of World Happines 2018 report will be used. The data set is downloaded from here. The original data set is in Microsoft Excel format. It has been extracted and saved in csv file called WHData-2018.csv.
Importing Data
In the code chunk below, read_csv() of readr is used to import WHData-2018.csv into R and parsed it into tibble R data frame format.
wh <-read_csv("data/WHData-2018.csv")
Preparing the data
Change the rows by country name instead of row number by using the code chunk below
row.names(wh) <- wh$Country
Note
Notice that the row number has been replaced into the country name.
Transforming the data frame into a matrix
The data was loaded into a data frame, but it has to be a data matrix to make the heatmap.
The code chunk below will be used to transform wh data frame into a data matrix.
There are many R packages and functions can be used to drawing static heatmaps, they are:
heatmap()of R stats package. It draws a simple heatmap.
heatmap.2() of gplots R package. It draws an enhanced heatmap compared to the R base function.
pheatmap() of pheatmap R package. pheatmap package also known as Pretty Heatmap. The package provides functions to draws pretty heatmaps and provides more control to change the appearance of heatmaps.
ComplexHeatmap package of R/Bioconductor package. The package draws, annotates and arranges complex heatmaps (very useful for genomic data analysis). The full reference guide of the package is available here.
superheat package: A Graphical Tool for Exploring Complex Datasets Using Heatmaps. A system for generating extendable and customizable heatmaps for exploring complex datasets, including big data and data with multiple data types.
By default, heatmap() plots a cluster heatmap. The arguments Rowv=NA and Colv=NA are used to switch off the option of plotting the row and column dendrograms.
The order of both rows and columns is different compared to the native wh_matrix. This is because heatmap does a reordering using clusterisation: it calculates the distance between each pair of rows and columns and try to order them by similarity. Moreover, the corresponding dendrogram are provided beside the heatmap.
Here, red cells denote small values. This heatmap is not really informative. Indeed, the Happiness Score variable have relatively higher values, what makes that the other variables with small values all look the same. Thus, this matrix needs to be normalised. This is done using the scale argument. It can be applied to rows or to columns.
The code chunk below normalises the matrix column-wise.
Note that the values are scaled now. Also note that margins argument is used to ensure that the entire x-axis labels are displayed completely and, cexRow and cexCol arguments are used to define the font size used for y-axis and x-axis labels respectively.
Creating Interactive Heatmap
heatmaply is an R package for building interactive cluster heatmap that can be shared online as a stand-alone HTML file. It is designed and maintained by Tal Galili.
The code chunk below shows the basic syntax needed to create n interactive heatmap by using heatmaply package.
heatmaply(wh_matrix[, -c(1, 2, 4, 5)])
Note
Note:
Different from heatmap(), for heatmaply() the default horizontal dendrogram is placed on the left hand side of the heatmap.
The text label of each raw, on the other hand, is placed on the right hand side of the heat map.
When the x-axis marker labels are too long, they will be rotated by 135 degree from the north.
Data Trasformation
When analysing multivariate data sets, it is very common that the variables include values that reflect different types of measurements. In general, these variable values have their own range. In order to ensure that all the variables have comparable values, data transformation is commonly used before clustering.
Three main data transformation methods are supported by heatmaply(), namely: scale, normalise and percentilise.
Scaling method
When all variables come from or are assumed to come from a normal distribution, then scaling (i.e.: subtract the mean and divide by the standard deviation) would bring them all closer to the standard normal distribution.
In such a case, each value would reflect the distance from the mean in units of standard deviation.
The scale argument in heatmaply() supports column and row scaling.
The code chunk below is used to scale variable values columewise.
When variables in the data come from different (and non-normal) distributions, the normalize function can be used to bring data to the 0 to 1 scale by subtracting the minimum and dividing by the maximum of all observations.
This preserves the shape of each variable’s distribution while making them easily comparable on the same “scale”.
Different from Scaling, the normalise method is performed on the input data set i.e. wh_matrix as shown in the code chunk below.
This is similar to ranking the variables, but instead of keeping the rank values, they are divided by the maximal rank.
This is done by using the ecdf of the variables on their own values, bringing each value to its empirical percentile.
The benefit of the percentize function is that each value has a relatively clear interpretation, it is the percent of observations that got that value or below it.
Similar to Normalize method, the Percentize method is also performed on the input data set i.e. wh_matrix as shown in the code chunk below.
heatmaply supports a variety of hierarchical clustering algorithm. The main arguments provided are:
distfun: function used to compute the distance (dissimilarity) between both rows and columns. Defaults to dist. The options “pearson”, “spearman” and “kendall” can be used to use correlation-based clustering, which uses as.dist(1 - cor(t(x))) as the distance metric (using the specified correlation method).
hclustfun: function used to compute the hierarchical clustering when Rowv or Colv are not dendrograms. Defaults to hclust.
dist_method default is NULL, which results in “euclidean” to be used. It can accept alternative character strings indicating the method to be passed to distfun. By default distfun is “dist”” hence this can be one of “euclidean”, “maximum”, “manhattan”, “canberra”, “binary” or “minkowski”.
hclust_method default is NULL, which results in “complete” method to be used. It can accept alternative character strings indicating the method to be passed to hclustfun. By default hclustfun is hclust hence this can be one of “ward.D”, “ward.D2”, “single”, “complete”, “average” (= UPGMA), “mcquitty” (= WPGMA), “median” (= WPGMC) or “centroid” (= UPGMC).
In general, a clustering model can be calibrated either manually or statistically.
Manual approach
In the code chunk below, the heatmap is plotted by using hierachical clustering algorithm with “Euclidean distance” and “ward.D” method.
One of the problems with hierarchical clustering is that rows do not have a definite order, it merely constrains the space of possible orderings. For example, 3 itmes A, B, and C have three possible orderings: ABC, ACB and BAC. If clustering them gives ((A+B)+C) as a tree, it is clear that C can’t end up between A and B, but there is no information as to which way to flip the A+B cluster. It is unknown if the ABC ordering will lead to a clearer-looking heatmap compared to the BAC ordering.
heatmaply uses the seriation package to find an optimal ordering of rows and columns. Optimal means to optimise the Hamiltonian path length that is restricted by the dendrogram structure. This means to rotate the branches so that the sum of distances between each adjacent leaf (label) will be minimised. This is related to a restricted version of the travelling salesman problem.
Optimal Leaf Ordering (OLO) starts with the output of an agglomerative clustering algorithm and produces a unique ordering, one that flips the various branches of the dendrogram around so as to minimise the sum of dissimilarities between adjacent leaves. Here is the result of applying Optimal Leaf Ordering to the same clustering result as the heatmap above.
The default options is “OLO” (Optimal leaf ordering) which optimizes the above criterion (in O(n^4)). Another option is “GW” (Gruvaeus and Wainer) which aims for the same goal but uses a potentially faster heuristic.
The default colour palette used by heatmaply is viridis. heatmaply users, however, other colour palettes can be used to to improve the aestheticness and visual friendliness of the heatmap.
In the code chunk below, the Blues colour palette of rColorBrewer is used.
Beside providing a wide collection of arguments for meeting the statistical analysis needs, heatmaply also provides many plotting features to ensure cartographic quality heatmap can be produced.
In the code chunk below the following arguments are used:
k_row is used to produce 5 groups.
margins is used to change the top margin to 60 and row margin to 200.
fontsizw_row and fontsize_col are used to change the font size for row and column labels to 4.
main is used to write the main title of the plot.
xlab and ylab are used to write the x-axis and y-axis labels respectively.
