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)
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.
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 \(h(A) \le h(B)\) 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 \(u_{ij} \le \max(u_{ik}, u_{jk})\) 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.
hcl <- hclust(dist(USArrests))
is.cl_dendrogram(hcl)
is.cl_hierarchy(hcl)
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