Hierarchies
Description
Determine whether an R object represents a hierarchy of objects, or coerce to an R object representing such.
Usage
1 2 3 4 5 
Arguments
x 
an R object. 
Details
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 ntrees
(hierarchies in the strict sense) and dendrograms (also known
as valued ntrees or total indexed hierarchies), which are
represented by the virtual classes "cl_hierarchy"
and
"cl_dendrogram"
(which inherits from the former),
respectively.
ntrees 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 ntrees where additionally a height h is associated with each of the classes, so that for two classes A and B with nonempty 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 (3point) 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.
Value
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
.
Examples
1 2 3 