Find an optimal linear leaf ordering of a binary merge tree as produced by a hierarchical cluster algorithm.

1 |

`dist` |
an object of class |

`merge` |
a binary merge tree (see |

A binary tree has *2^(n-1)* internal nodes (subtrees) and
the same
number of leaf orderings. That is, at each internal node the left
and right subtree (or leaves) can be swapped, or, in terms of a
dendrogram, be flipped.

An objective measure of a leaf ordering is the sum of the distances along the path connecting the leaves in the given order. An ordering with a minimal path length is defined to be an optimal ordering.

This function provides an interface to the optimal leaf ordering
algorithm (see references) for tree representations that are used by
hierarchical cluster algorithms such as `hclust`

.

Note that non-finite distance values are not allowed.

A list with the following components:

`merge` |
a matrix containing the merge tree corresponding with the optimal leaf order. |

`order` |
a vector containing the optimal leaf order. |

`length` |
the length of the ordering. |

The time complexity of the algorithm is *O(n^3)*.

Christian Buchta

Z. Bar-Joseph, E. D. Demaine, D. K. Gifford, and T. Jaakkola.
(2001). Fast Optimal Leaf Ordering for Hierarchical Clustering.
*Bioinformatics*, Vol. 17 Suppl. 1, pp. 22-29.

`hclust`

for hierarchical clustering and
`order.length`

for computing the objective value of a
leaf ordering.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ```
d <- dist(matrix(runif(30), ncol=2))
hc <- hclust(d)
co <- order.optimal(d, hc$merge)
### compare dendrograms
ho <- hc
ho$merge <- co$merge
ho$order <- co$order
op <- par(mfrow=c(2,2), pty="s")
plot(hc, main="hclust")
plot(ho, main="optimal")
# compare images
implot(d[[hc$order]])
implot(d[[co$order]])
par(op)
### compare lengths
order.length(d, hc$order)
order.length(d, co$order)
cat("compare: ",co$length,"\n")
``` |

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