Function spantree finds a minimum spanning tree
connecting all points, but disregarding dissimilarities that are at or
above the threshold or NA.
spantree(d, toolong = 0)
# S3 method for spantree
as.hclust(x, ...)
# S3 method for spantree
cophenetic(x)
spandepth(x)
# S3 method for spantree
plot(x, ord, cex = 0.7, type = "p", labels, dlim,
FUN = sammon, ...)
# S3 method for spantree
lines(x, ord, display="sites", col = 1, ...)Function spantree
returns an object of class spantree which is a
list with two vectors, each of length \(n-1\). The
number of links in a tree is one less the number of observations, and
the first item is omitted. The items are
The child node of the parent, starting from parent number
two. If there is no link from the parent, value will be NA
and tree is disconnected at the node.
Corresponding distance. If kid = NA, then
dist = 0.
Names of nodes as found from the input dissimilarities.
The function call.
Dissimilarity data inheriting from class dist or
a an object, such as a matrix, that can be converted to a
dissimilarity matrix. Functions vegdist and
dist are some functions producing suitable
dissimilarity data.
Shortest dissimilarity regarded as NA.
The function uses a fuzz factor, so
that dissimilarities close to the limit will be made NA, too.
If toolong = 0 (or negative), no dissimilarity is regarded
as too long.
A spantree result object.
An ordination configuration, or an ordination result known
by scores.
Character expansion factor.
Observations are plotted as points with
type="p" or type="b", or as text label with
type="t". The tree (lines) will always be plotted.
Text used with type="t" or node names if this is
missing.
A ceiling value used to highest cophenetic dissimilarity.
Ordination function to find the configuration from
cophenetic dissimilarities. If the supplied FUN does not work,
supply ordination result as argument ord.
Type of scores used for ord.
Colour of line segments. This can be a vector which is recycled for points, and the line colour will be a mixture of two joined points.
Other parameters passed to functions.
Jari Oksanen
Function spantree finds a minimum spanning tree for
dissimilarities (there may be several minimum spanning trees, but the
function finds only one). Dissimilarities at or above the threshold
toolong and NAs are disregarded, and the spanning tree
is found through other dissimilarities. If the data are disconnected,
the function will return a disconnected tree (or a forest), and the
corresponding link is NA. Connected subtrees can be identified
using distconnected.
Minimum spanning tree is closely related to single linkage
clustering, a.k.a. nearest neighbour clustering, and in genetics as
neighbour joining tree available in hclust and
agnes functions. The most important practical
difference is that minimum spanning tree has no concept of cluster
membership, but always joins individual points to each other. Function
as.hclust can change the spantree result into a
corresponding hclust object.
Function cophenetic finds distances between all points along
the tree segments. Function spandepth returns the depth of
each node. The nodes of a tree are either leaves (with one link) or
internal nodes (more than one link). The leaves are recursively
removed from the tree, and the depth is the layer at with the leaf
was removed. In disconnected spantree object (in a forest)
each tree is analysed separately and disconnected nodes not in any
tree have depth zero.
Function plot displays the tree over a
supplied ordination configuration, and lines adds a spanning
tree to an ordination graph. If configuration is not supplied for plot,
the function ordinates the cophenetic dissimilarities of the
spanning tree and overlays the tree on this result. The default
ordination function is sammon (package MASS),
because Sammon scaling emphasizes structure in the neighbourhood of
nodes and may be able to beautifully represent the tree (you may need
to set dlim, and sometimes the results will remain
twisted). These ordination methods do not work with disconnected
trees, but you must supply the ordination configuration. Function
lines will overlay the tree in an existing plot.
Function spantree uses Prim's method
implemented as priority-first search for dense graphs (Sedgewick
1990). Function cophenetic uses function
stepacross with option path = "extended". The
spantree is very fast, but cophenetic is slow in very
large data sets.
Sedgewick, R. (1990). Algorithms in C. Addison Wesley.
data(dune)
dis <- vegdist(dune)
tr <- spantree(dis)
## Add tree to a metric scaling
plot(tr, cmdscale(dis), type = "t")
## Find a configuration to display the tree neatly
plot(tr, type = "t")
## Depths of nodes
depths <- spandepth(tr)
plot(tr, type = "t", label = depths)
## Plot as a dendrogram
cl <- as.hclust(tr)
plot(cl)
## cut hclust tree to classes and show in colours in spantree
plot(tr, col = cutree(cl, 5), pch=16)
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