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Distance matrix methods fit a tree to a matrix of pairwise
distances between the sequences. Most distance methods use some
form of weighted or unweighted least squares measure. Given are the distances
d_{ij}. The problem is to find distances
such that
the score of the tree is
minimized. The score of a tree is often defined as:

(1) 
where where p can be set to 0, 1 or 2. The methods assume
that the variance of the measurement error is proportional to the
pth power of the expectation. The only rigorous way to get an
optimal solution is by trying out all tree topologies. For a given
tree topology, this least squares problem leads to a system of
linear equations which can be solved using standard methods of
numerical linear algebra. However, finding the optimal topology is
generally an intractable problem, since the number of tree
topologies grows exponentially with the number of nodes.
Chantal Korostensky
19990714