A New Quartet Tree Heuristic for Hierarchical Clustering
Data Structures and Algorithms2011-11-09v1Computer Vision and Pattern RecognitionDiscrete MathematicsStatistics TheoryData Analysis, Statistics and ProbabilityQuantitative MethodsStatistics Theory
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.
@article{arxiv.cs/0606048,
title = {A New Quartet Tree Heuristic for Hierarchical Clustering},
author = {Rudi Cilibrasi and Paul M. B. Vitanyi},
journal= {arXiv preprint arXiv:cs/0606048},
year = {2011}
}