The Geometry of the Neighbor-Joining Algorithm for Small Trees

@inproceedings{Eickmeyer2008TheGO,
  title={The Geometry of the Neighbor-Joining Algorithm for Small Trees},
  author={Kord Eickmeyer and Ruriko Yoshida},
  booktitle={Algebraic Biology},
  year={2008}
}
In 2007, Eickmeyer et al. showed that the tree topologies outputted by the Neighbor-Joining (NJ) algorithm and the balanced minimum evolution (BME) method for phylogenetic reconstruction are each determined by a polyhedral subdivision of the space of dissimilarity maps ${\mathbb R}^{n \choose 2}$, where nis the number of taxa. In this paper, we will analyze the behavior of the Neighbor-Joining algorithm on five and six taxa and study the geometry and combinatorics of the polyhedral subdivision… 
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Combinatorial and Computational Investigations of Neighbor-Joining Bias

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Optimality of the Neighbor Joining Algorithm and Faces of the Balanced Minimum Evolution Polytope

It is proved that any subtree-prune-regraft move from a binary tree to another binary tree corresponds to an edge of the BME polytope, and an entire family of faces parameterized by disjoint clades are described, showing that these clade-faces are smaller dimensional BMEpolytopes themselves.

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On the optimality of the neighbor-joining algorithm

The l2 radius for neighbor-joining for n = 5 is obtained and the ability of the neighbor- joining algorithm to recover the BME tree depends on the diameter of the B ME tree.

Bayes estimators for phylogenetic reconstruction

In this work, a unified framework of BE trees is discussed, focusing especially on tree distances that are expressible as squared euclidean distances, and it is shown that BEs can be estimated in practice by hill-climbing and tends to be closer to the true tree compared with ML and neighbor joining.

Mathematical and Simulation-Based Analysis of the Behavior of Admixed Taxa in the Neighbor-Joining Algorithm

The neighbor-joining algorithm for phylogenetic inference has been seen to have three specific properties when applied to distance matrices that contain an admixed taxon, but it is observed that these properties are sometimes violated by distanceMatrices that include an admixture.

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The l2 radius for neighbor-joining for n = 5 is obtained and the ability of the neighbor- joining algorithm to recover the BME tree depends on the diameter of the B ME tree.

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Abstract We show that the neighbor-joining algorithm is a robust quartet method for constructing trees from distances. This leads to a new performance guarantee that contains Atteson’s optimal radius…

The Performance of Neighbor-Joining Methods of Phylogenetic Reconstruction

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