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 <[email protected]> Sent: Monday, August 25, 2025 12:28 AM To: Leo Mada via R-help <[email protected]> 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 [[alternative HTML version deleted]]
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