Friday, May 28, 2021

Maximum entropy summary trees to display higher classifications

A challenge in working with large taxonomic classifications is how you display them to the user, especially if the user probably doesn't want all the gory details. For example, the Field Guide app to Victorian Fauna has a nice menu of major animal groups:

This includes both taxonomic and ecological categories (e.g., terrestrial, freshwater, etc.) and greatly simplifies the animal tree of life, but it is a user-friendly way to start browsing a larger database of facts about animals. It would be nice if we could automate constructing such lists, especially for animal groups where the choices of what to display might not seem obvious (everyone wants to see birds, but what insects groups would you prioritise?).

One way to help automate these sort of lists is to use summary trees (see also Karloff, H., & Shirley, K. E. (2013). Maximum Entropy Summary Trees. Computer Graphics Forum, 32(3pt1), 71–80. doi:10.1111/cgf.12094). A summary tree takes a large tree and produces a small summary for k nodes, where< i>k is a number that you supply. In other words, if you want your summary to have 10 nodes then k=10. The diagram below summarises an organisation chart for 43,134 employees.

Summary trees show only a subset of the nodes in the complete tree. All the nodes with a given parent that aren't displayed get aggregated into a newly created "others" node that is attached to that parent. Hence the summary tree alerts the user that there are nodes which list in the full tree but which aren't shown.

Code for maximum entropy summary trees is available in C and R from https://github.com/kshirley/summarytrees, so I've been playing with it a little (I don't normally use R but there was little choice here). As an example I created a simple tree for animals, based on the Catalogue of Life. I took a few phyla and classes and built a tree as a CSV file (see the gist). The file lists each node (uniquely numbered), its parent node (the parent of the root of the tree is "0"), a label, and a weight. For an internal node the weight is always 0, for a leaf the weight can be assigned in various ways. By default you could assign each leaf a weight of 1, but if the "leaf" node represents more than one thing (for example, the class Mammalia) then you can give it the number of species in that class (e.g., 5939). You could also assign weights based on some other measure, such as "popularity". In the gist I got bored and only added species counts for a few taxa, everything else was set to 1.

I then loaded the tree into R and found a summary tree for k=30 (the script is in the gist):

This doesn't look too bad (note as I said above, I didn't fill in all the actual species counts because reasons). If I wanted to convert this into a menu such as the one the Victoria Fauna app uses I would simply list the leaf nodes in order, skipping over those labelled "n others", which would give me:

  • Mammalia
  • Amphibia
  • Reptilia
  • Aves
  • Actinopterygii
  • Hemiptera
  • Hymenoptera
  • Lepidoptera
  • Diptera
  • Coleoptera
  • Arachnida
  • Acanthocephala
  • Nemertea
  • Rotifera
  • Porifera
  • Platyhelminthes
  • Nematoda
  • Mollusca

These 18 taxa are not a bad starting point for a menu, especially if we added pictures from PhyloPic to liven it up. There are probably a couple of animal groups that could be added to make it a bit more inclusive.

Because the technique is automated and fast, it would be straightforward to create submenus for major taxa, with the added advantage that you don't beed to make decisions based whether you know anything about that taxonomic group, it can be driven entirely by species counts (for example). We could also use other measures for weights, such as number of Google search hits, size of pages on Wikipedia, etc. So far I've barely scratched the surface of what could be done with this tool.

P.S. The R code is:

library(devtools)
install_github("kshirley/summarytrees", build_vignettes = TRUE)

library(summarytrees)

data = read.table('/Users/rpage/Development/summarytrees/animals.csv', header=TRUE,sep=",")

g <- greedy(node = data[, "node"], 
            parent = data[, "parent"], 
            weight = data[, "weight"], 
            label = data[, "label"], 
            K = 30)
            write.csv(g$summary.trees[[30]], '/Users/rpage/Development/summarytrees/summary.csv') 

The gist has the data file, and a simple PHP program to convert the output into a dot file to be viewed with GraphViz.