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A New Quartet Tree Heuristic for Hierarchical Clustering

Rudi Cilibrasi·Paul M. B. Vitanyi
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Abstract

We consider the problem of constructing an an optimal-weight tree from the 3*(n choose 4) weighted quartet topologies on n objects, where optimality means that the summed weight of the embedded quartet topologiesis optimal (so it can be the case that the optimal tree embeds all quartets as non-optimal topologies). We present a heuristic for reconstructing the optimal-weight tree, and a canonical manner to derive the quartet-topology weights from a given distance matrix. The method repeatedly transforms a bifurcating tree, with all objects involved as leaves, achieving a monotonic approximation to the exact single globally optimal tree. This contrasts to other heuristic search methods from biological phylogeny, like DNAML or quartet puzzling, which, repeatedly, incrementally construct a solution from a random order of objects, and subsequently add agreement values.

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Rudi Cilibrasi, Paul M. B. Vitanyi. 2006-06-11. A New Quartet Tree Heuristic for Hierarchical Clustering. https://arxiv.org/abs/cs/0606048

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