hierarchy | R Documentation |
Determine whether an R object represents a hierarchy of objects, or coerce to an R object representing such.
is.cl_hierarchy(x) is.cl_dendrogram(x) as.cl_hierarchy(x) as.cl_dendrogram(x)
x |
an R object. |
These functions are generic functions.
The methods provided in package clue handle the partitions and hierarchies obtained from clustering functions in the base R distribution, as well as packages RWeka, ape, cba, cclust, cluster, e1071, flexclust, flexmix, kernlab, mclust, movMF and skmeans (and of course, clue itself).
The hierarchies considered by clue are n-trees
(hierarchies in the strict sense) and dendrograms (also known
as valued n-trees or total indexed hierarchies), which are
represented by the virtual classes "cl_hierarchy"
and
"cl_dendrogram"
(which inherits from the former),
respectively.
n-trees on a set X of objects correspond to collections H of subsets of X, usually called classes of the hierarchy, which satisfy the following properties:
H contains all singletons with objects of X, X itself, but not the empty set;
The intersection of two sets A and B in H is either empty or one of the sets.
The classes of a hierarchy can be obtained by
cl_classes
.
Dendrograms are n-trees where additionally a height h is associated with each of the classes, so that for two classes A and B with non-empty intersection we have h(A) ≤ h(B) iff A is a subset of B. For each pair of objects one can then define u_{ij} as the height of the smallest class containing both i and j: this results in a dissimilarity on X which satisfies the ultrametric (3-point) conditions u_{ij} ≤ \max(u_{ik}, u_{jk}) for all triples (i, j, k) of objects. Conversely, an ultrametric dissimilarity induces a unique dendrogram.
The ultrametric dissimilarities of a dendrogram can be obtained by
cl_ultrametric
.
as.cl_hierarchy
returns an object of class
"cl_hierarchy"
“containing” the given object x
if
this already represents a hierarchy (i.e., is.cl_hierarchy(x)
is true), or the ultrametric obtained from x
via
as.cl_ultrametric
.
as.cl_dendrogram
returns an object which has class
"cl_dendrogram"
and inherits from "cl_hierarchy"
,
and contains x
if it represents a dendrogram (i.e.,
is.cl_dendrogram(x)
is true), or the ultrametric obtained from
x
.
Conceptually, hierarchies and dendrograms are virtual classes, allowing for a variety of representations.
There are group methods for comparing dendrograms and computing their
minimum, maximum, and range based on the meet and join operations, see
cl_meet
. There is also a plot
method.
For the testing functions, a logical indicating whether the given object represents a clustering of objects of the respective kind.
For the coercion functions, a container object inheriting from
"cl_hierarchy"
, with a suitable representation of the hierarchy
given by x
.
hcl <- hclust(dist(USArrests)) is.cl_dendrogram(hcl) is.cl_hierarchy(hcl)
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