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`dendrogram` General Tree Structures

Description

Class "dendrogram" provides general functions for handling tree-like structures. It is intended as a replacement for similar functions in hierarchical clustering and classification/regression trees, such that all of these can use the same engine for plotting or cutting trees.

Usage

as.dendrogram(object, ...)
## S3 method for class 'hclust'
as.dendrogram(object, hang = -1, check = TRUE, ...)

## S3 method for class 'dendrogram'
as.hclust(x, ...)

## S3 method for class 'dendrogram'
plot(x, type = c("rectangle", "triangle"),
      center = FALSE,
      edge.root = is.leaf(x) || !is.null(attr(x,"edgetext")),
      nodePar = NULL, edgePar = list(),
      leaflab = c("perpendicular", "textlike", "none"),
      dLeaf = NULL, xlab = "", ylab = "", xaxt = "n", yaxt = "s",
      horiz = FALSE, frame.plot = FALSE, xlim, ylim, ...)

## S3 method for class 'dendrogram'
cut(x, h, ...)

## S3 method for class 'dendrogram'
merge(x, y, ..., height,
      adjust = c("auto", "add.max", "none"))

## S3 method for class 'dendrogram'
nobs(object, ...)

## S3 method for class 'dendrogram'
print(x, digits, ...)

## S3 method for class 'dendrogram'
rev(x)

## S3 method for class 'dendrogram'
str(object, max.level = NA, digits.d = 3,
    give.attr = FALSE, wid = getOption("width"),
    nest.lev = 0, indent.str = "",
    last.str = getOption("str.dendrogram.last"), stem = "--",
    ...)

is.leaf(object)

Arguments

`object`	any R object that can be made into one of class `"dendrogram"`.
`x, y`	object(s) of class `"dendrogram"`.
`hang`	numeric scalar indicating how the height of leaves should be computed from the heights of their parents; see `plot.hclust`.
`check`	logical indicating if `object` should be checked for validity. This check is not necessary when `x` is known to be valid such as when it is the direct result of `hclust()`. The default is `check=TRUE`, e.g. for protecting against memory explosion with invalid inputs.
`type`	type of plot.
`center`	logical; if `TRUE`, nodes are plotted centered with respect to the leaves in the branch. Otherwise (default), plot them in the middle of all direct child nodes.
`edge.root`	logical; if true, draw an edge to the root node.
`nodePar`	a `list` of plotting parameters to use for the nodes (see `points`) or `NULL` by default which does not draw symbols at the nodes. The list may contain components named `pch`, `cex`, `col`, `xpd`, and/or `bg` each of which can have length two for specifying separate attributes for inner nodes and leaves. Note that the default of `pch` is `1:2`, so you may want to use `pch = NA` if you specify `nodePar`.
`edgePar`	a `list` of plotting parameters to use for the edge `segments` and labels (if there's an `edgetext`). The list may contain components named `col`, `lty` and `lwd` (for the segments), `p.col`, `p.lwd`, and `p.lty` (for the `polygon` around the text) and `t.col` for the text color. As with `nodePar`, each can have length two for differentiating leaves and inner nodes.
`leaflab`	a string specifying how leaves are labeled. The default `"perpendicular"` write text vertically (by default). `"textlike"` writes text horizontally (in a rectangle), and `"none"` suppresses leaf labels.
`dLeaf`	a number specifying the distance in user coordinates between the tip of a leaf and its label. If `NULL` as per default, 3/4 of a letter width or height is used.
`horiz`	logical indicating if the dendrogram should be drawn horizontally or not.
`frame.plot`	logical indicating if a box around the plot should be drawn, see `plot.default`.
`h`	height at which the tree is cut.
`height`	height at which the two dendrograms should be merged. If not specified (or `NULL`), the default is ten percent larger than the (larger of the) two component heights.
`adjust`	a string determining if the leaf values should be adjusted. The default, `"auto"`, checks if the (first) two dendrograms both start at `1`; if they do, code"add.max" is chosen, which adds the maximum of the previous dendrogram leaf values to each leaf of the “next” dendrogram. Specifying `adjust` to another value skips the check and hence is a tad more efficient.
`xlim, ylim`	optional x- and y-limits of the plot, passed to `plot.default`. The defaults for these show the full dendrogram.
`..., xlab, ylab, xaxt, yaxt`	graphical parameters, or arguments for other methods.
`digits`	integer specifying the precision for printing, see `print.default`.
`max.level, digits.d, give.attr, wid, nest.lev, indent.str`	arguments to `str`, see `str.default()`. Note that `give.attr = FALSE` still shows `height` and `members` attributes for each node.
`last.str, stem`	strings used for `str()` specifying how the last branch (at each level) should start and the stem to use for each dendrogram branch. In some environments, using `last.str = "'"` will provide much nicer looking output, than the historical default last.str = "`".

Details

The dendrogram is directly represented as a nested list where each component corresponds to a branch of the tree. Hence, the first branch of tree z is z[[1]], the second branch of the corresponding subtree is z[[1]][[2]], or shorter z[[c(1,2)]], etc.. Each node of the tree carries some information needed for efficient plotting or cutting as attributes, of which only members, height and leaf for leaves are compulsory:

members: total number of leaves in the branch
height: numeric non-negative height at which the node is plotted.
midpoint: numeric horizontal distance of the node from the left border (the leftmost leaf) of the branch (unit 1 between all leaves). This is used for plot(*, center = FALSE).
label: character; the label of the node
x.member: for cut()$upper, the number of former members; more generally a substitute for the members component used for ‘horizontal’ (when horiz = FALSE, else ‘vertical’) alignment.
edgetext: character; the label for the edge leading to the node
nodePar: a named list (of length-1 components) specifying node-specific attributes for points plotting, see the nodePar argument above.
edgePar: a named list (of length-1 components) specifying attributes for segments plotting of the edge leading to the node, and drawing of the edgetext if available, see the edgePar argument above.
leaf: logical, if TRUE, the node is a leaf of the tree.

cut.dendrogram() returns a list with components $upper and $lower, the first is a truncated version of the original tree, also of class dendrogram, the latter a list with the branches obtained from cutting the tree, each a dendrogram.

There are [[, print, and str methods for "dendrogram" objects where the first one (extraction) ensures that selecting sub-branches keeps the class, i.e., returns a dendrogram even if only a leaf. On the other hand, [ (single bracket) extraction returns the underlying list structure.

Objects of class "hclust" can be converted to class "dendrogram" using method as.dendrogram(), and since R 2.13.0, there is also a as.hclust() method as an inverse.

rev.dendrogram simply returns the dendrogram x with reversed nodes, see also reorder.dendrogram.

The merge(x, y, ...) method merges two or more dendrograms into a new one which has x and y (and optional further arguments) as branches. Note that before R 3.1.2, adjust = "none" was used implicitly, which is invalid when, e.g., the dendrograms are from as.dendrogram(hclust(..)).

nobs(object) returns the total number of leaves (the members attribute, see above).

is.leaf(object) returns logical indicating if object is a leaf (the most simple dendrogram).

plotNode() and plotNodeLimit() are helper functions.

Warning

Some operations on dendrograms such as merge() make use of recursion. For deep trees it may be necessary to increase options("expressions"): if you do, you are likely to need to set the C stack size (Cstack_info()[["size"]]) larger than the default where possible.

Note

plot():: When using type = "triangle", center = TRUE often looks better.
str(d):: If you really want to see the internal structure, use str(unclass(d)) instead.

Examples

require(graphics); require(utils)

hc <- hclust(dist(USArrests), "ave")
(dend1 <- as.dendrogram(hc)) # "print()" method
str(dend1)          # "str()" method
str(dend1, max.level = 2, last.str =  "'") # only the first two sub-levels
oo <- options(str.dendrogram.last = "\\") # yet another possibility
str(dend1, max.level = 2) # only the first two sub-levels
options(oo)  # .. resetting them

op <- par(mfrow =  c(2,2), mar = c(5,2,1,4))
plot(dend1)
## "triangle" type and show inner nodes:
plot(dend1, nodePar = list(pch = c(1,NA), cex = 0.8, lab.cex = 0.8),
      type = "t", center = TRUE)
plot(dend1, edgePar = list(col = 1:2, lty = 2:3),
     dLeaf = 1, edge.root = TRUE)
plot(dend1, nodePar = list(pch = 2:1, cex = .4*2:1, col = 2:3),
     horiz = TRUE)

## simple test for as.hclust() as the inverse of as.dendrogram():
stopifnot(identical(as.hclust(dend1)[1:4], hc[1:4]))

dend2 <- cut(dend1, h = 70)
## leaves are wrong horizontally in R 4.0 and earlier:
plot(dend2$upper)
plot(dend2$upper, nodePar = list(pch = c(1,7), col = 2:1))
##  dend2$lower is *NOT* a dendrogram, but a list of .. :
plot(dend2$lower[[3]], nodePar = list(col = 4), horiz = TRUE, type = "tr")
## "inner" and "leaf" edges in different type & color :
plot(dend2$lower[[2]], nodePar = list(col = 1),   # non empty list
     edgePar = list(lty = 1:2, col = 2:1), edge.root = TRUE)
par(op)
d3 <- dend2$lower[[2]][[2]][[1]]
stopifnot(identical(d3, dend2$lower[[2]][[c(2,1)]]))
str(d3, last.str = "'")

## to peek at the inner structure "if you must", use '[..]' indexing :
str(d3[2][[1]]) ## or the full
str(d3[])

## merge() to join dendrograms:
(d13 <- merge(dend2$lower[[1]], dend2$lower[[3]]))
## merge() all parts back (using default 'height' instead of original one):
den.1 <- Reduce(merge, dend2$lower)
## or merge() all four parts at same height --> 4 branches (!)
d. <- merge(dend2$lower[[1]], dend2$lower[[2]], dend2$lower[[3]],
            dend2$lower[[4]])
## (with a warning) or the same using  do.call :
stopifnot(identical(d., do.call(merge, dend2$lower)))
plot(d., main = "merge(d1, d2, d3, d4)  |->  dendrogram with a 4-split")

## "Zoom" in to the first dendrogram :
plot(dend1, xlim = c(1,20), ylim = c(1,50))

nP <- list(col = 3:2, cex = c(2.0, 0.75), pch =  21:22,
           bg =  c("light blue", "pink"),
           lab.cex = 0.75, lab.col = "tomato")
plot(d3, nodePar= nP, edgePar = list(col = "gray", lwd = 2), horiz = TRUE)

addE <- function(n) {
      if(!is.leaf(n)) {
        attr(n, "edgePar") <- list(p.col = "plum")
        attr(n, "edgetext") <- paste(attr(n,"members"),"members")
      }
      n
}
d3e <- dendrapply(d3, addE)
plot(d3e, nodePar =  nP)
plot(d3e, nodePar =  nP, leaflab = "textlike")

dendrogram General Tree Structures