Dear R Users, This is a follow-up to one of my older messages. Although I did not receive useful suggestions back then, I did some research on my own and found an R package and some references in the literature. I hope that this information is useful to others as well. ### Tree Balance The problem can be solved using indexes that measure the tree balance. Package mdendro implements 2 such indexes (chaining coefficient and a tree balance coefficient, which is actually the entropy of the tree structure). https://cran.r-project.org/web/packages/mdendro/index.html The paper referenced by mdendro is in the meantime published as well (it was not accessible a few days ago): Fern?ndez, A., & G?mez, S. (2025). mdendro: An R Package for Extended Agglomerative Hierarchical Clustering. Journal of Statistical Software, 114(2), 1?26. https://doi.org/10.18637/jss.v114.i02 The other reference is much older (and I do not have access to it): Williams W, Lambert J, Lance G (1966). ?Multivariate Methods in Plant Ecology: V. Similarity Analyses and Information-Analysis.? Journal of Ecology, 54(2), 427?445. doi: 10.2307/2257960. [it may be possible to read online, but not download the article; I have not fully checked] I have included some functions in my own R code on GitHub, like index.chaining and index.entropy: https://github.com/discoleo/PeptideClassifier/blob/main/R/Helper.Tree.Analysis.R I hope this info is useful to others as well. Sincerely, Leonard Initial Message: https://stat.ethz.ch/pipermail/r-help/2025-August/481164.html
From: Leo Mada <leo.mada at syonic.eu>
Sent: Monday, August 25, 2025 12:28 AM
To: Leo Mada via R-help <r-help at r-project.org>
Subject: Branch Ratios & other Indexes for Trees/Dendrograms
Sent: Monday, August 25, 2025 12:28 AM
To: Leo Mada via R-help <r-help at r-project.org>
Subject: Branch Ratios & other Indexes for Trees/Dendrograms
Dear R-Users,
I have another question regarding trees (dendrograms).
After exploring the various hierarchical clustering methods, it seems that some of the methods (average, single, median) add sequentially very small clusters (even 1 leaf) to an increasingly larger branch.
I would like to quantify this more rigorously. I do not think that banner plots fully capture this fact, as they are limited to height of the node where a leaf binds.
I came up with 2 alternative measures:
- Ratio of leaves on 1 branch (larger branch) vs the other branch (see function branch.ratios);
- Size of other branch of the node where 1 leaf binds;
The latter resembles the bannerplot; and is also limited only to nodes with leaves.
Can anyone point me to such indexes in the literature and/or in other R packages?
I am not an expert in the field. Searching for cluster indexes will likely generate a huge number of false positive results (i.e. indexes for number of clusters).
An example of this functionality is given below:
# Pre-computed Trees:
x1 = readRDS("Tree.Full.M_ward.D.rds")
x2 = readRDS("Tree.Full.M_average.rds")
br1 = branch.ratios(x1)
br2 = branch.ratios(x2)
# Alternative: size.leafBranch(x1);
par.old = par(mfrow = c(1,2))
hist(br1);
# Branch Ratio goes up to 1300!
hist(br2);
par(par.old)
# Note: Median & centroid are even more extreme!
The data sets and functions are on GitHub:
https://github.com/discoleo/PeptideClassifier/tree/main/inst/examples
Functions: branch.ratios, size.leafBranch, count.nodes;
https://github.com/discoleo/PeptideClassifier/blob/main/R/Helper.Tree.R
I have attached an image to this mail with all 8 histograms. The image is also available on GitHub:
https://github.com/discoleo/PeptideClassifier/blob/main/Trees.BranchRatios.png
Many thanks in advance,
Leonard