hierarchy {clue}

Hierarchies

Description

Determine whether an R object represents a hierarchy of objects, or coerce to an R object representing such.

Usage

is.cl_hierarchy(x)
is.cl_dendrogram(x)

as.cl_hierarchy(x)
as.cl_dendrogram(x)

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 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.

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

hcl <- hclust(dist(USArrests))
is.cl_dendrogram(hcl)
is.cl_hierarchy(hcl)