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Tree comparison using Laplacian spectra


Dear babblers,

I stumbled across today. This paper attempts yet another method of summarising trees, this time using what the authors call “Spectral Density Profiles”, which are just [if I understood correctly] a transformation of the eigen values of the patristic distance matrix.

This seems to me like a principled way of introducing branch lengths in, for example, the [sprspace] ( framework: one could store the set of spectra for a particular topology in a hashmap and then use those to inform clustering on the SPR graph. The communities in the graph would then be not only a result of their proximity in the topological space, but also on “branch length space”. Their methods are even implemented as an R package, RPANDA.

I’m looking specially at you, @ematsen, @cwhidden, @mathmomike and @mtholder.




That’s an interesting paper, Max, and thanks for pointing it out.

It’s worth keeping in mind that any matrix-determinant-based methods are invariant to leaf relabeling, so this is a measure of tree shape rather than labeled topology. This could still be a useful key for a hash map, though I bet that we could cook up something using labels that would be even more informative.

The following paper does not have branch lengths as part of the definition of the spectra, but it shows some limitations of such an approach. Branch lengths will increase overlap.


Its interesting. I think, as a paleontologically-inclined person, one of the more intriguing things about this manuscript is its applications for analyzing diversification patterns on non-ultrametric phylogenies, which (as the paper points out) have been sorely lacking from the macroevolutionary toolbox.